Edit orial
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v3.1

Acknowledgments
This book could never have been created without the dedication
and collective expertise of the staff and students of The Princeton
Review.
Many thanks to Jonathan Chiu, the National Content Director for
High School Programs.
Many thanks also to Chris Aylward, Brian Becker, Lisa Mayo, Amy
Minster, Elizabeth Owens, and Stephen Shuck for their
contributions in developing the content for this title.
Special thanks to Claudia Landgrover for masterfully managing the
development and review processes for this title.
Special thanks also to Adam Robinson, who conceived of and
perfected the Joe Bloggs approach to standardized tests as well as
many other successful techniques used by The Princeton Review.

Contents
Cover
Title Page
Copyright
Acknowledgments
…So Much More Online!

Part I: Orientation
1 Introduction
2 All About National Merit Scholarships

Part II: Practice Test
3 Practice Test 1
4 Practice Test 1: Answers and Explanations

Part III: Drills
5 Drills
6 Drills: Answers and Explanations

Part IV: Practice Tests
7
8
9
10

Practice Test
Practice Test
Practice Test
Practice Test

2
2: Answers and Explanations
3
3: Answers and Explanations

…So Much More Online!
More Practice…
Free SAT online demonstration with a full-length practice SAT
and interactive lessons

More Good Stuff…
PSAT at-a-glance overview
Articles on SAT techniques to get you ready for the next step

…then College!
Detailed profiles for hundreds of colleges help you find the
school that is right for you
Dozens of Top 10 ranking lists including Quality of Professors,
Worst Campus Food, Most Beautiful Campus, Party Schools,
Diverse Student Population, and tons more
Useful information about the admissions process
Helpful information about financial aid and scholarships

Part I
Orientation

Chapter 1
Introduction

Who Writes the PSAT?

The PSAT is written and administered by Educational Testing
Service (ETS), under contract by the College Board. You might think
that the people at ETS are educators, professors of education, or
teachers. They are not. The people who work for ETS are average
people who just happen to make a living writing tests. In fact, they
write hundreds of tests, for all kinds of organizations. They are a
group of “testers-for-hire” who will write a test for anyone who asks.
The folks at ETS are not paid to educate; they are paid to write and
administer tests. Furthermore, even though you will be paying ETS
to take the PSAT, you are not their customer. The actual customers
ETS caters to are the colleges, who get the information they want at
no cost. This means that you should take everything that ETS says
with a grain of salt and realize that its testing “advice” is not always
the best advice. (Getting testing advice from ETS is a bit like getting
baseball advice from the opposing team.)
Every test reflects the interests of the people who write it. If you
know who writes the test, you will know a lot more about what
kinds of answers will be considered “correct” answers on that test.

What Is The Princeton Review?

The Princeton Review is the nation’s leading test-preparation
company. In just a few years, we became the nation’s leader in SAT
preparation, primarily because our techniques work. We offer
courses and private tutoring for all of the major standardized tests,
and we publish a series of books to help in your search for the right
school. If you would like more information about how The Princeton
Review can help you, go to PrincetonReview.com or call 800-2Review.

Short cut s
The Princeton Review’s
techniques are the closest
thing there is to a shortcut
to the PSAT. However,
there is no shortcut to
learning these techniques.

How to Use this Book

This book is divided into three main parts. The first part of the book
is a practice test that will give you an idea of your strengths and
weaknesses, both of which can be sources of improvement. If you’re
already good at something, additional practice can make you great
at it; if you’re not so good at something, what you should do about it
depends on how important it is.
The second part of the book contains the different sections of a fulllength PSAT so that you can practice on timing or content or both!
Focus on the problems that gave you trouble in the first test in this
book. If you ultimately decide that you would like more practice,
our Cracking the PSAT edition can give the additional work that you
seek.
The third part of the book contains two additional full-length PSATs
for you to use for evaluative purposes.

When You Take a Practice Test

Here are some guidelines for taking these tests:
Time yourself strictly. Use a timer, watch, or stopwatch that will
ring, and do not allow yourself to go over time for any section.
If you try to do so at the real test, your scores will likely be
canceled.

Take a practice test in one sitting, allowing yourself breaks of no
more than two minutes between sections. You need to build up
your endurance for the real test, and you also need an accurate
picture of how well you will do.
Always take a practice test using an answer sheet with bubbles
to fill in, just as you will for the real test. For the practice tests
in the book, use the attached answer sheets. You need to be
comfortable transferring answers to the separate sheet because
you will be skipping around a bit.
Each bubble you choose should be filled in thoroughly, and no
other marks should be made in the answer area.
As you fill in the bubble for a question, check to be sure you are
on the correct number on the answer sheet. If you fill in the
wrong bubble on the answer sheet, it will not matter if you
worked out the problem correctly in the test booklet. All that
matters to the machine scoring the test is the No. 2 pencil mark.

Chapter 2
All About National Merit
Scholarships
The NMSQT part of the name PSAT/NMSQT stands for National
Merit Scholarship Qualifying Test. That means that the PSAT serves
as the test that will establish whether or not you are eligible for
National Merit recognition. This chapter will help you figure out
what that may mean for you.

How Do I Qualify for National Merit?

To qualify for any National Merit recognition, you must:
Be a U.S. citizen or permanent resident who intends to become a
U.S. citizen
Be enrolled full-time in high school
Take the PSAT in the third year of high school (for four-year
programs; slightly different rules apply if you are in a three-year
program or other course of study)
Be fully endorsed and recommended for a Merit scholarship by
your high school principal
Have a record of strong academic performance throughout high
school
Complete the National Merit Scholarship Corporation (NMSC)
Scholarship Application
Obtain high scores on the SAT, which you will take later in the
year

The Index

How does your PSAT score qualify you for National Merit? The
National Merit Scholarship Corporation uses a selection index, which
is the sum of your Math, Critical Reading, and Writing Skills scores.
For instance, if your PSAT scores were 60 Math, 50 Critical Reading,
and 60 Writing Skills, your index would be 170.
Math + Critical Reading + Writing Skills = National Merit Index
60

+

50

+

60

=

170

The Awards and the Process

In the fall of their senior year, about 50,000 students will receive
one of two letters from NMSC: either a Letter of Commendation or a
letter stating that they have qualified as semifinalists for National
Merit.
Commended Students
Roughly two-thirds of these students
(about 34,000 total students each year) will receive a Letter of
Commendation by virtue of their high scores on the test. This looks
great on your college application, so if you have a reasonable chance
of receiving this recognition, it is definitely worth your time to
prepare for the PSAT. Make no mistake, though, these letters are not
easy to get. They are awarded to students who score between the
95th and the mid-99th percentiles—that means to the top three
percent in the country.
If you receive this honorable mention from NMSC, you should be
extremely proud of yourself. Even though you will not continue in
the process for National Merit scholarships, this commendation does
make you eligible for special scholarships sponsored by certain
companies and organizations, which vary in their amounts and
eligibility requirements.
Semifinalists
The other third of these students—those 16,000
students who score in the upper 99th percentile in their states—will
be notified that they are National Merit semifinalists. If you qualify,
you will receive a letter announcing your status as a semifinalist,
along with information about the requirements for qualification as a
finalist. These include maintaining high grades, performing well on
your SAT, and getting an endorsement from your principal.
Becoming a National Merit semifinalist is quite impressive, and if
you manage it, you should certainly mention it on your college
applications.

What does “scoring in the upper 99th percentile in the state” mean?
It means that you’re essentially competing against the other people
in your state for those semifinalist positions. Since some states have
higher average scores than others, this means that if you’re in states
like New York, New Jersey, Maryland, Connecticut, or
Massachusetts, you need a higher score to qualify than if you live in
other states. However, the majority of the indices are in the range of
200–215. (This means approximate scores of 70 Critical Reading, 70
Math, 70 Writing Skills.)
Many students want to know exactly what score they need. Sadly,
National Merit is notoriously tight-lipped about these numbers. It
releases them only on rare occasions and generally does not like to
announce them. However, it is not difficult to obtain some pretty
reliable unofficial data on what it takes to be a semifinalist. Below
you will find the most up-to-date qualifying scores for the class of
2013 National Merit semifinalists:

Note, however, that while these numbers are probably roughly the
same from year to year, they do change to a certain degree. These
should be used only to give you a rough idea of the range of scores
for National Merit recognition.
Finalists The majority of semifinalists (more than 90 percent) go
on to qualify as finalists. Students who meet all of the eligibility
requirements will be notified in February of their senior year that

they have qualified as finalists. This means that they are now
eligible for scholarship money, though it does not necessarily mean
that they will receive any. In fact, only about half of National Merit
finalists actually win scholarships. What determines whether a
student is awarded money or not? There is a final screening process,
based on criteria that NMSC does not release to the public, to
determine who actually receives these scholarships. This year, there
will be 8,300 Merit Scholarship winners and 1,300 Special
Scholarship recipients. Unlike the Merit Scholarships, which are
given by the NMSC, the Special Scholarship recipients will receive
awards from corporate sponsors and are selected from students who
are outstanding, but not National Merit finalists.
Though the amounts of money are not huge, every little bit helps,
and the award itself looks very impressive in your portfolio. So if
you think you are in contention for National Merit recognition, study
hard. If not, don’t sweat it too much, but do prepare for the PSAT
because it is good practice for the SAT.

What If I Miss the PSAT Administration My
Junior Year?

If you are not concerned about National Merit scholarships, there is
no reason to do anything in particular—except, perhaps, to obtain a
few PSAT booklets to practice on, just to see what fun you missed.
However, if you want to be eligible for National Merit recognition,
then swift action on your part is required. If an emergency arises
that prevents you from taking the PSAT, you should write to the
National Merit Scholarship Corporation immediately to request
alternate testing dates. If your request is received soon enough, it
should be able to accommodate you. (NMSC says that this kind of
request must absolutely be received by March 1 following the missed
PSAT administration.) You will also need a signature from a school

official.

For More Information

If you have any questions or problems, the best person to consult is
your school guidance counselor, who can help make sure you are on
the right track. If you need further help, contact your local Princeton
Review office at 800-2-REVIEW or PrincetonReview.com. Or, you
can contact National Merit directly:
National Merit Scholarship Corporation
1560 Sherman Avenue, Suite 200
Evanston, IL 60201-4897
(847) 866-5100
NationalMerit.org

Part II
Practice Test

Chapter 3
Practice Test 1
Click here to download a PDF of Practice Test 1

SECTION 1
Time — 25 minutes
24 Questions
(1-24)
Directions: For each question in this section, select the best answer from among the
choices given and fill in the corresponding circle on the answer sheet.

Each sentence below has one or two blanks, each blank indicating that something has
been omitted. Beneath the sentence are five words or sets of words labeled A through
E. Choose the word or set of words that, when inserted in the sentence, best fits the
meaning of the sentence as a whole.
Example:

Desiring to ------- his taunting friends, Mitch gave them taffy in hopes it would keep
their mouths shut.

(A) eliminate (B) satisfy (C) overcome (D) ridicule (E) silence

1. Excited about ------- new cooking techniques, Raquel pored over cookbooks and
bought a few important kitchen utensils.

(A) resisting (B) mitigating (C) entertaining (D) neglecting
(E) investigating

2. By successfully publishing poems, short stories, and novels throughout his
career, the author proved himself to have a ------- writing ability.

(A) finite (B) radical (C) diversified (D) middling (E) visionary

3. Although the armadillo has armor-like scales that form a shield over its

3. Although the armadillo has armor-like scales that form a shield over its

shoulders, back, and hips, its ------- underside is covered only with skin and
fur.

(A) guarded (B) vulnerable (C) complex (D) youthful (E) sallow
4. The return home for failed Olympic hopeful Cecily Carter was -------: she was
happy to see everyone but ------- to explain why she hadn’t made the team.
(A) exhilarating . . depressed
(B) distressing . . hesitant
(C) ambivalent . . amused
(D) inconvenient . . challenged
(E) bittersweet . . loath
5. Many large-pot lottery winners, lacking the financial savvy to appropriately
deal with such a(n) -------, eventually wind up -------.
(A) deficiency . . thriving
(B) insight . . ingenious
(C) paucity . . bankrupt
(D) windfall . . insolvent
(E) abundance . . illustrious
6. Rarely -------, Juan tended to demand his way with those he worked with,
never bothering to consult or ask anyone else’s opinion.

(A) synergistic (B) imperious (C) overbearing (D) extroverted (E) disjointed

7. Many in the film industry considered the producer the ------- of -------; he was

7. Many in the film industry considered the producer the ------- of -------; he was
the quintessential professional.

(A) paragon . . malevolence
(B) connoisseur . . immaturity
(C) extension . . accomplishment
(D) epitome . . proficiency
(E) personification . . philanthropy
8. Knitters apprehensive about attempting more intricate patterns will be

motivated by Lee Hartwell’s ------- instructional videos, which ------- even the
trickiest stitches.

(A) abstruse . . obscure
(B) munificent . . critique
(C) straightforward . . muddle
(D) vocational . . explicate
(E) pellucid . . demystify

The passages below are followed by questions based on their content; questions

following a pair of related passages may also be based on the relationship between the

paired passages. Answer the questions on the basis of what is stated or implied in the
passage and in any introductory material that may be provided.
Questions 9-12 are based on the following passages.

9. Both authors do which of the following in these passages?
(A) Incorporate critics’ reviews.
(B) Write in the first person.
(C) Mention specific films.
(D) Refer to the reader’s romantic experiences.
(E) Refute the arguments of others.
10. In line 17 the word “cheesy” most nearly means
(A) genuine
(B) shoddy
(C) melted
(D) inauthentic
(E) charming
11. The author of Passage 1 would most likely respond to the “detractors”
(Passage 2, line 23) with
(A) total approval
(B) mild frustration
(C) sarcasm
(D) hesitancy
(E) resentment

12. Which best captures the attitude of each author toward romantic comedies?

12. Which best captures the attitude of each author toward romantic comedies?
(A) The author of Passage 1 feels romantic comedies are less realistic than

they used to be, whereas the author of Passage 2 thinks they are a good
bargain.

(B) The author of Passage 1 is slightly bored by the improbability of the
films, whereas the author of Passage 2 is completely fed up with it.

(C) The author of Passage 1 disdains the phoniness of romantic comedies,
whereas the author of Passage 2 supposes them to be accurate
representations of real life.

(D) The author of Passage 1 is frustrated by the unrealistic standards set in
romantic comedies, whereas the author of Passage 2 enjoys the
optimistic consistency of the films.

(E) The author of Passage 1 is annoyed by the recent increase in movie

ticket prices, whereas the author of Passage 2 believes the films help
people feel optimistic about their lives.

Questions 13-24 are based on the following passage.
This passage is adapted from a book published in 2012.

13. The first paragraph (lines 1-7) most directly focuses on the
(A) predicted downfall of internet search engines
(B) death of true research in contemporary scholarship
(C) distinction between topics of old scholarship and new
(D) reduction of intelligence in the modern age
(E) contemporary availability of large amounts of information

14. In context, the reference to “previous generations of scholars” (lines 4-5) is

14. In context, the reference to “previous generations of scholars” (lines 4-5) is
significant in that it

(A) demonstrates the contrast between old and new methods of research
(B) states that people from earlier eras had more time to spend reading
(C) emphasizes the contemporary scholar’s contempt for libraries
(D) indicates the accuracy provided by basic internet searches
(E) shows that new research methods can reveal universal knowledge
15. In line 11, the phrase “information saturation” describes the
(A) mode of thinking that has crippled contemporary research methods
(B) contrast between effective and ineffective methods of acquiring
information

(C) moment at which an intelligent human being can no longer learn new
information

(D) change in contemporary thinking about the usefulness of scholarly
research

(E) emerging situation in which information becomes too much for one
person to know

16. In lines 12-13, “at … behest” most nearly means
(A) under our control
(B) beyond our understanding
(C) in our books
(D) available to us
(E) within our grasp

17. In lines 15-16, “our understanding” represents a shift away from

17. In lines 15-16, “our understanding” represents a shift away from
(A) online databases
(B) universal knowledge
(C) inadequate explanations
(D) faith-based interpretations
(E) a knowable world
18. The author mentions “researchers” (line 24) and “a scholar” (line 25)
primarily to

(A) underline the importance of traditional modes of study
(B) warn against the dangers of traditional research
(C) wonder at the importance of printed books
(D) compare the researchers of previous ages unfavorably to those of today
(E) demonstrate instances of one type of study
19. In context, the book cited in line 26 supports the notion that
(A) the scope of contemporary research has changed
(B) scholars no longer have ambitious research goals
(C) the study of mythology has disappeared from contemporary scholarship
(D) one particular book answers more questions than the internet can
(E) researchers are more accurate when they work with limited information

20. The author suggests that “Now” (line 29) scholars have become

20. The author suggests that “Now” (line 29) scholars have become
(A) hopeless
(B) collaborative
(C) inundated
(D) smarter
(E) aggressive
21. In lines 38-42 (“Indeed … foreign”), the author notes a parallel between
(A) contemporary research and the makeup of mall food courts
(B) a desire for complete knowledge and cultural and ethnic diversity
(C) the amount of information and the excesses of consumerism
(D) trends in research and preferences for foreign goods
(E) the range of available information and economic globalization
22. The word “witchcraft” (line 55) refers to
(A) one of the new forms of information available to contemporary scholars
(B) a recently developed power made possible by internet searching
(C) lives lived in an era without modern conveniences
(D) the ability to experience many parts of the world in a single place
(E) the overwhelming amount of information that is available at all times

23. The example of the “computer-savvy researcher” (line 63) is primarily used to

23. The example of the “computer-savvy researcher” (line 63) is primarily used to
illustrate

(A) rampant procrastination
(B) technological sophistication
(C) deep knowledge
(D) mental handicaps
(E) informational availability
24. The primary purpose of the last paragraph (lines 66-86) is to
(A) doubt that the new modes of acquiring information will ever generate
important discoveries

(B) suggest that some compromise is possible between old and new ways of
acquiring information

(C) long for an earlier mode of research that relied on the deep study of
long printed books

(D) defend the rights of computer-literate people to use whatever bits of
information they find relevant

(E) outline the differences between those who use computers to access
information and those who do not

ST OP
If you finish before time is called, you may check your work on
this section only.
Do not turn to any other section in the test.

SECTION 2
Time — 25 minutes
20 Questions
(1-20)
Directions: For this section, solve each problem and decide which is the best of the
choices given. Fill in the corresponding circle on the answer sheet. You may use any
available space for scratchwork.

Notes
1. The use of a calculator is permitted.
2. All numbers used are real numbers.
3. Figures that accompany problems in this test are intended to provide information
useful in solving the problems. They are drawn as accurately as possible

EXCEPT when it is stated in a specific problem that the figure is not drawn to
scale. All figures lie in a plane unless other wise indicated.

4. Unless otherwise specified, the domain of any function f is assumed to be the set
of all real numbers x for which f(x) is a real number.

Reference Information

The number of degrees of arc in a circle is 360.
The sum of the measures in degrees of the angles of a triangle is 180.

1. If y + 3 = 7, what is the value of 2y + 3 ?

1. If y + 3 = 7, what is the value of 2y + 3 ?
(A)

–5

(B)

8

(C) 11
(D) 14
(E) 23

2. In the figure above, which side of 5-sided polygon ABCDE has the greatest
negative slope?
(A) EA
(B) AB
(C) BC
(D) CD
(E) DE

3. Rhys has a bucket of candy containing 15 lollipops, 25 gumballs, 35 licorice

3. Rhys has a bucket of candy containing 15 lollipops, 25 gumballs, 35 licorice
sticks, and no other types of candy. If Rhys selects one type of candy at

random, what is the probability that the chosen candy will be a licorice stick?
(A)
(B)
(C)
(D)
(E)

4. If (b + 2)(3b – 6) = z, then (b + 2)(b – 2) =
(A)

z

(B)

z

(C)

z

(D) 3z
(E) 6z

5. If three lines intersect to form six equal angles, what is the measure of one of
these angles?
(A) 15°
(B) 30°
(C) 45°
(D) 50°
(E) 60°

6. Brian surveyed the 18 students in his algebra class to determine the amount of
time they spent doing homework and the number of questions answered on

the last test. The scatterplot above shows the homework time and the number
of test questions answered for each of the 18 students. Line m is the best fit

line. For how many students was the number of test questions answered fewer
than what the best fit line predicted for the corresponding homework time?
(A) 8
(B) 9
(C) 10
(D) 11
(E) 13

7. The expression 3p + 6 could be represented by which of the following

7. The expression 3p + 6 could be represented by which of the following
operations?

(A) 3 times 6 more than a number p
(B) 3 times 6 less than a number p
(C) 3 more than 6 times a number p
(D) 6 less than 3 times a number p
(E) 6 more than 3 times a number p

8. If the quantity (2t – 5) is divisible by t, which of the following could be the
value of t ?
(A) 4
(B) 5
(C) 6
(D) 7
(E) 8

9. In the figure above, AD = DB = EC = CF. If ΔABC and ΔDEF are equilateral,
and AB = 10, what is the perimeter of quadrilateral CGDH ?
(A) 10
(B) 15
(C) 20
(D) 25
(E) 35

10. Helene lists her zip code on an application form. She notices that the first and
last digits are both prime, the middle digit is a divisor of 45, and the least
common multiple of remaining two digits is 6. Which of the following
numbers could be her zip code?
(A) 22935
(B) 23924
(C) 32437
(D) 35563
(E) 52732

11. What number is 4 less than

of itself?

(A) –11
(B) –10
(C)

–9

(D)

–8

(E)

–6

12. Ringo is a dog that is not brown. From which of the following statements can
it be determined whether or not Ringo is a Labrador?

(A) Any dog that is not brown is not a Labrador.
(B) Some dogs that are brown are not Labradors.
(C) All dogs that are brown are Labradors.
(D) No dogs are both brown and Labradors.
(E) Any dog that is brown is not a Labrador.

13. The side of square S is twice the diameter of circle C. What is the greatest

possible number of points of intersection of the perimeter of square S and the
circumference of circle C ?
(A) Two
(B) Three
(C) Four
(D) Six
(E) Eight

y = –x

y = –x

y=x+n
14. If the ordered pair (t, 2), where x = t and y = 2, is the intersection of the two
lines above, then what is the value of n ?
(A)

–2

(B)

0

(C)

2

(D)

4

(E)

6

15. The graph above shows the number of widgets made by two machines, F and
G, plotted against the number of hours in operation. On average, for each
hour of operation, how many more widgets did machine G make than
machine F?
(A)

9

(B) 10
(C) 22
(D) 50
(E) 60

16. If w is an integer and 8 is a factor of 2w, which of the following must be true?
I. w is an even integer
II. w is divisible by 4
III. w is divisible by 8
(A) I only
(B) II only
(C) I and II only
(D) II and III only
(E) I, II, and III

17. If q and s are greater than 0 and

= s5, then =

(A) q5
(B) q6
(C) q10
(D) q12
(E) q20

18. Line l, defined by the equation x + 2y = 4, is graphed in the xy-plane. Line m
is the reflection of line l across the x-axis. Which is the following is an
equation of line m ?

(A) x – 2y = –4
(B) x + 2y = –4
(C) x – 2y = 4
(D) x + 2y = 4
(E) 2x – y = –2

19. A lock requires a 3-digit code such that each digit is a positive even number
less than 9. How many such codes are possible?
(A)

4

(B)

8

(C) 16
(D) 24
(E) 64

20. The figure above shows a square with side of length 4. The center of the

square, point O, is also the center of circle O, with radius 1. Four semicircles

with radius 1 are centered on each side of the square. If the arcs shown have
centers at A, B, C, and D, what is the area of the shaded region?
(A) 4π
(B) 16
(C) 8π – 8
(D) 8 + 4π
(E) 16 – 2π

ST OP
If you finish before time is called, you may check your work on
this section only.
Do not turn to any other section in the test.

SECTION 3
Time — 25 minutes
24 Questions
(25-48)
Directions: For each question in this section, select the best answer from among the
choices given and fill in the corresponding circle on the answer sheet.

Each sentence below has one or two blanks, each blank indicating that something has
been omitted. Beneath the sentence are five words or sets of words labeled A through
E. Choose the word or set of words that, when inserted in the sentence, best fits the
meaning of the sentence as a whole.
Example:

Hoping to ------- the dispute, negotiators proposed a compromise that they felt would
be ------- to both labor and management.
(A) enforce . . useful
(B) end . . divisive
(C) overcome . . unattractive
(D) extend . . satisfactory
(E) resolve . . acceptable

25. Though the training methods were rigorous and exhausting, the results were
so ——– that the athletes kept up with the program.

(A) calming (B) astonishing (C) disastrous (D) subtle (E) brutal

26. Among the hundreds of siblings in professional football are brothers Peyton

26. Among the hundreds of siblings in professional football are brothers Peyton

and Eli Manning, both quarterbacks but with ——– throwing styles: while Eli
has a much stronger arm, Peyton is the more accurate passer.

(A) uniform (B) vigorous (C) complicated (D) trendy (E) distinct
27. The novice jungle explorers were concerned about getting lost in the

rainforest, but the maps they brought were so ------- that their fears of never
returning from the expedition were much -------.
(A) meticulous . . alleviated
(B) vibrant . . justified
(C) systematic . . exacerbated
(D) inaccurate . . lightened
(E) antiquated . . panicked

28. Although the pufferfish is the second-most ------- vertebrate on the planet,
producing toxins that can kill a human within 24 hours, its big eyes and
comically rotund appearance ------- its lethality.
(A) virulent . . communicate
(B) distended . . belie
(C) poisonous . . witness
(D) toxiferous . . disaffirm
(E) trafficable . . ridicule
29. The article described the appearance of goose bumps under stress as a ------reflex because for our ancestors, having their hair stand on end made them

look more intimidating to would-be predators, but for modern humans, there
is really no purpose for the reaction.

(A) genealogical (B) defunct (C) primitive (D) pedantic
(E) vestigial

The passages below are followed by questions based on their content; questions

following a pair of related passages may also be based on the relationship between the

paired passages. Answer the questions on the basis of what is stated or implied in the
passage and in any introductory material that may be provided.
Questions 30-31 are based on the following passage.

*U.S. President 1801-1809
30. The author indicates that the “others” (line 5) view Jefferson as a man who
(A) practiced what he preached
(B) had strong political aspirations
(C) believed all men are created equal
(D) had a significant amount of land
(E) said one thing but did another

31. The primary purpose of this passage is to

31. The primary purpose of this passage is to
(A) summarize Thomas Jefferson’s political career
(B) concede Thomas Jefferson’s role in the slave trade
(C) present varying perspectives on Thomas Jefferson
(D) challenge Thomas Jefferson’s status as an eminent politician
(E) connect Thomas Jefferson’s political success to his financial success
Questions 32-33 are based on the following passage.

32. The author uses “ingenuously” (line 5) to mean that online shoppers
(A) accidentally use the wrong credit card
(B) don’t understand how the Internet works
(C) deliberately use wrong information to throw off thieves
(D) don’t realize their information is insecure
(E) are savvy about how they make online purchases

33. The author cites the figure of “9 million” (lines 8-9) in order to suggest that

33. The author cites the figure of “9 million” (lines 8-9) in order to suggest that
(A) using a credit card is safer than using a debit card
(B) large retailers are less secure than smaller retailers
(C) some victims of identity theft have had information stolen multiple
times

(D) the FTC keeps meticulous data about online hackers
(E) online shopping is less secure than many shoppers might think

Questions 34-39 are based on the following passage.
Each passage below discusses rabies. Passage 1 was published in July 2012; Passage 2
was published in October 2012.

34. In their discussion of rabies, the authors of Passage 1 and Passage 2 each make
use of

(A) recent findings and theories from medical researchers
(B) emotionally charged addresses to the reader
(C) complex metaphors and figurative language
(D) citations from amateur rabies researchers
(E) descriptions of the brain’s chemical makeup

35. The mention of the “human diploid cell rabies vaccine” (Passage 1, lines 2-3)

35. The mention of the “human diploid cell rabies vaccine” (Passage 1, lines 2-3)

and “the initial protocol” (Passage 2, line 36) would best support the idea that
(A) rabies can be cured with an induced coma and a combination of
medicines

(B) rabies is predominantly incurable after a certain stage
(C) the effects of rabies on the brain cannot be reversed
(D) rabies was curable for a short period but is no longer curable
(E) other diseases similar to rabies are not so damaging to the brain
36. The primary purpose of Passage 2 is to
(A) underline the importance of debate within the scientific community
(B) offer a warning that recent scientific findings are not fully conclusive
(C) detail the ways in which the brain’s chemistry is resistant to induced
coma

(D) warn against the deteriorating effects of the Milwaukee protocol
(E) praise the recent discoveries of Dr. Willoughby and others in the field
37. The author of Passage 2 would most likely respond to the findings discussed in
Passage 1 with

(A) agreement, given his general appreciation for advances in medical
science

(B) dismissal, because he disagrees so strongly with the Milwaukee protocol
(C) skepticism, since the research presented have not been adequately
proven

(D) shock, because the statistics are so precisely aligned with his own
argument

(E) grudging approval, since the findings in the first passage are so
conclusive

38. If the sample of “25 treated patients” (Passage 2, line 37) had a greater

38. If the sample of “25 treated patients” (Passage 2, line 37) had a greater

survival rate, the greater rate would most likely have had what effect on the
author’s argument in Passage 1?

(A) Strengthen the argument by providing additional statistical support
(B) Weaken the argument by showing a fault in the argument’s logic
(C) Provide an insoluble contradiction to the argument with empirical data
(D) Reduce the coherence of the argument by introducing new data
(E) No effect, because the findings have already been dismissed by the
author of Passage 1

39. The evidence provided about rabies cures in Passage 1 and Passage 2,
respectively, is best described as

(A) encouraging vs. disputed
(B) fantastic vs. grounded
(C) scientific vs. anecdotal
(D) amateurish vs. medical
(E) mature vs. irrelevant

Questions 40-48 are based on the following passage.
This passage is adapted from a 2009 novel set in Egypt and the United Kingdom.

40. The first two paragraphs (line 1-30) primarily suggest that Naim was
(A) more interested in becoming a celebrity than in improving his skills
(B) working to change his game to be more consistent with what his coach
suggested

(C) exasperated by his attempts to become a great squash player
(D) wishing that he had become a tennis player
(E) contemptuous of his squash coach

41. In line 11, the word “that” refers to which of the following from lines 1-10?

41. In line 11, the word “that” refers to which of the following from lines 1-10?
(A) Naim’s difficult training regimen
(B) Naim’s wavering devotion to the sport of squash
(C) Naim’s inability to become a great player
(D) The overreaction to a loss in tournament play
(E) The talented players against whom Naim played
42. The parenthetical remarks in lines 20-21 anticipate which of the following in
the passage?

(A) Naim’s search for true inspiration
(B) Naim’s ultimate wish to give up squash for tennis
(C) Naim’s belief in the teachings of Mr. Shabana
(D) Naim’s choice to become a squash professional
(E) Naim’s admiration for Mohamed El Shorbagy
43. The sentence in lines 26-27 (“Naim … players”) indicates that Naim wanted to
(A) be listed among the great squash players of all time
(B) perfect the English style of playing squash
(C) appear on televised sporting events
(D) improve upon what Mr. Shabana advised
(E) show that his style of play could be learned by other players

44. Lines 29-30 (“where … stars”) suggest which of the following about Naim?

44. Lines 29-30 (“where … stars”) suggest which of the following about Naim?
(A) His appreciation of the English style of squash
(B) His egotism in believing that his style of squash is superior
(C) His level of admiration for well-known squash players
(D) The disappointment he would face if he were to switch to tennis
(E) His wish to be a unique and well-respected athlete
45. In line 30, “regimented” most nearly means
(A) military
(B) uncreative
(C) little-known
(D) difficult
(E) disciplined
46. The third paragraph (lines 31-50) primarily serves to
(A) show a renewal of interest
(B) highlight a willingness to mature
(C) defend a difficult choice
(D) cheer a series of victories
(E) concede an earlier point
47. What Naim found most appealing in El Shorbagy’s play was its
(A) expressive creativity
(B) disciplined form
(C) Egyptian squash style
(D) popular appeal
(E) technical perfection

48. The final paragraph most directly elaborates on which point made earlier by
the narrator?

(A) “his biggest challenge came from his coach” (line 11)
(B) “Naim couldn’t say” (line 23)
(C) “the best players were like movie stars” (line 30)
(D) “he found the inspiration he had been missing” (lines 32-33)
(E) “El Shorbagy played the traditional game” (lines 38-39)

ST OP
If you finish before time is called, you may check your work on
this section only.
Do not turn to any other section in the test.

SECTION 4
Time — 25 minutes
18 Questions
(21-38)

Directions: For this section, solve each problem and decide which is the best of the
choices given. Fill in the corresponding circle on the answer sheet. You may use any
available space for scratchwork.

Notes
1. The use of a calculator is permitted.
2. All numbers used are real numbers.
3. Figures that accompany problems in this test are intended to provide information
useful in solving the problems. They are drawn as accurately as possible

EXCEPT when it is stated in a specific problem that the figure is not drawn to
scale. All figures lie in a plane unless other wise indicated.

4. Unless otherwise specified, the domain of any function f is assumed to be the set
of all real numbers x for which f(x) is a real number.

Reference Information

The number of degrees of arc in a circle is 360.
The sum of the measures in degrees of the angles of a triangle is 180.

21. If r is an integer and 7.3 × 10r is a number between 8,000 and 80,000, what is
the value of r ?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5

22. In the xy-plane above, ABCD is a square with a side length of 8. If line m

passes through points A and C, which of the following points lies on line m ?
(A) (–5, 0)
(B) (0, –5)
(C) (–5, 5)
(D) (0, 5)
(E) (5, 5)

23. A total of 30,000 students attend College Q. How many of the students have a
GPA that is less than 4.0 ?
(A)

3,000

(B)

6,000

(C) 12,000
(D) 20,000
(E) 24,000

3, 15, 35, 63, …

3, 15, 35, 63, …
24. The sequence above is formed by multiplying each odd integer by the next odd
integer, starting with 1. What is the difference between the 7th and 8th term
of the sequence?
(A)

1

(B)

28

(C)

60

(D) 128
(E) 256

25. When Gilbert rents a car from the Cars4U dealership, he is charged a constant
rate per mile the car is driven plus a fixed cost for a carwash. On Monday he

was charged a total of $13 after driving the rental car for 20 miles. On Friday
he was charged $11.50 for driving the rental car 14 miles. Which of the

following equations expresses the total charge T, in dollars, when Gilbert
drives the rental car for m miles?
(A) T = m – 7
(B) T = 0.25m
(C) T = 0.25m + 8
(D) T = 0.5m + 4
(E) T = 8m + 0.50

26. The function g is defined by g(x) = 33 – 4x. If g(b) = 5, what is the value of b

26. The function g is defined by g(x) = 33 – 4x. If g(b) = 5, what is the value of b
?

(A) –
(B) –7
(C)

7

(D)
(E) 13

27. In the figure above, AB = 200 and BC = 5. Which of the following must be
true?

(A) r is less than s and t
(B) s is greater than r and t
(C) t is greater than r and s
(D) s is equal to t
(E) r is greater than s and t

28. At a certain department store, the only sizes of shirts sold are small, medium,

28. At a certain department store, the only sizes of shirts sold are small, medium,
and large. At that store, the ratio of small shirts to medium shirts is 5:2, and
the ratio of medium shirts to large shirts is 6:5. What is the ratio of small
shirts to all other shirts?
(A)

5:11

(B)

5:16

(C)

7:11

(D) 11:5
(E) 15:11

29. Each of the 8 salesmen at a used car dealership met his sales quota of 5 cars

last month. In addition, 3 of the salesmen each sold exactly 3 additional cars,
and 2 of the salesmen each sold 1 additional car. What is the total number of
cars sold by these 8 salesmen?

30. In 1976 the world record distance for throwing a discus was 230 feet, and by
1983 the record distance had increased to 235 feet and 3 inches. If the record
distance continues to increase at the same rate, in what year will the record
distance for throwing a discus reach 261

feet?

31. In the figure above, what is the value of z ?

32. In the figure above, AC and BD are the diagonals of rectangle ABCD. If x =
123, what is the value of z ?

33. In the graph above, h(x) is a quadratic function. For what x value does h(x)
reach its least value?

34. On her first four quizzes, Jan score 12, 8, 1, and 15 points. After Jan took her

fifth quiz, she found that the average (arithmetic mean) of the five quiz scores
was equal to the median of the five quiz scores. What is one possible value for
the number of points Jan scored on her fifth quiz?

35. On the number line above, the distance between point R and point S is 3. What
is the value of x ?

36. Sara created a list of 500 consecutive multiples of 4. What is the result if Sara

subtracts the smallest number in her list from the largest number her the list?

37. Four boards each measuring 2 inches by 4 inches by 12 inches are laid on a
flat floor to form a square, as shown in the figure on the left. Another four
boards of the same dimensions are laid on top of the first four in the same

way, as shown in the figure on the right. This process is repeated until the

boards are stacked a total of 10 boards high. The box created by these boards
is then filled with sand until the sand is perfectly level with the highest point
of the box. What is the volume, in cubic inches, of the sand in the box?

38. If 5 <

< 6, then what is one possible value of

?

ST OP
If you finish before time is called, you may check your work on
this section only.
Do not turn to any other section in the test.

SECTION 5
Time — 30 minutes
39 Questions
(1-39)

Directions: For each question in this section, select the best answer from among the
choices given and fill in the corresponding circle on the answer sheet.

The following sentences test correctness and effectiveness of expression. Part of each

sentence or the entire sentence is underlined; beneath each sentence are five ways of
phrasing the underlined material. Choice A repeats the original phrasing; the other

four choices are different. If you think the original phrasing produces a better sentence
than any of the alternatives, select choice A; if not, select one of the other choices.

In making your selection, follow the requirements of standard written English; that is,

pay attention to grammar, choice of words, sentence construction, and punctuation.
Your selection should result in the most effective sentence—clear and precise, without
awkwardness or ambiguity.
EXAMPLE:
Bobby Flay baked his first cake and he was thirteen years old then.
(A) and he was thirteen years old then
(B) when he was thirteen
(C) at age thirteen years old
(D) upon the reaching of thirteen years
(E) at the time when he was thirteen

1. One remarkable aspect of the platypus’ ankles is how it produces venom.
(A) how it produces
(B) the production of
(C) it produces
(D) when they produce
(E) by producing

2. Wuthering Heights is a dark, tragic novel, while it causes many of its readers to

2. Wuthering Heights is a dark, tragic novel, while it causes many of its readers to
shed tears.

(A) Wuthering Heights is a dark, tragic novel, while it
(B) Because Wuthering Heights is darkly tragic, and as such, it
(C) Being that it is a dark, tragic novel, Wuthering Heights
(D) Wuthering Heights, although a dark, tragic novel, it
(E) Wuthering Heights is a dark, tragic novel that
3. Having swum from Cuba to the United States, Diana Nyad became the first
individual to complete the journey without a shark cage, even though she
received multiple jellyfish stings.

(A) Having swum from Cuba to the United States, Diana Nyad
(B) Swimming from Cuba to the United States, Diana Nyad she
(C) When Diana Nyad swam from Cuba to the United States, so she
(D) Diana Nyad having swum from Cuba to the United States, and she
(E) To swim from Cuba to the United States, Diana Nyad
4. Jessica decided to take the bus rather than the train for the simple reason that
it was much less expensive in cost than the train that she could take.

(A) that it was much less expensive in cost than the train that she could
take.

(B) because the train was much more expensive.
(C) that it was much less expensive than the train.
(D) being that the train was much more expensive.
(E) of it being much less expensive than the train.

5. In 1958 Chinua Achebe attempted to print his novel Things Fall Apart, sending

5. In 1958 Chinua Achebe attempted to print his novel Things Fall Apart, sending
the manuscript to several publishers, some of them rejected it immediately.
(A) some of them
(B) that, out of some
(C) some of whom
(D) and some which
(E) some of those people
6. Of the many works of art from the Renaissance period, Leonardo da Vinci’s
oddly compelling Mona Lisa is more famous.

(A) oddly compelling Mona Lisa is more
(B) odd, compelling Mona Lisa is more
(C) Mona Lisa is oddly compelling, plus most
(D) Mona Lisa, which is oddly compelling, is the more
(E) oddly compelling Mona Lisa is the most
7. It was more probably disease and a lack of supplies than cold weather that
hindered Napoleon’s troops from successfully conquering Russia.
(A) Napoleon’s troops from successfully conquering Russia
(B) Russia being successfully conquered by Napoleon’s troops
(C) Napoleon’s troops to successfully conquer Russia
(D) Napoleon’s troops having successfully conquered Russia
(E) the successful conquering of Russia by Napoleon’s troops

8. In 1783, while only thirteen years old, three piano sonatas composed by

8. In 1783, while only thirteen years old, three piano sonatas composed by
Ludwig van Beethoven established his reputation as a musical prodigy.

(A) three piano sonatas composed by Ludwig van Beethoven established
(B) three piano sonatas that Ludwig van Beethoven composed established
(C) three piano sonatas were composed by Ludwig van Beethoven,
establishing

(D) Ludwig van Beethoven composed three piano sonatas, they established
(E) Ludwig van Beethoven composed three piano sonatas that established
9. If Xavier had regularly completed his physics assignments, he will be more
likely to succeed in the class.

(A) had regularly completed his physics assignments
(B) regularly completes his physics assignments
(C) could regularly complete what he is assigned in physics
(D) can regularly complete what he is assigned in physics
(E) could have regularly completed his physics assignments
10. After digging for several years, the discovery of King Tutankhamun’s tomb by

Howard Carter and George Herbert sparked renewed interest in ancient Egypt.
(A) the discovery of King Tutankhamun’s tomb by Howard Carter and
George Herbert sparked renewed interest in ancient Egypt

(B) the discovering of King Tutankhamun’s tomb by Howard Carter and
George Herbert sparked renewed interest in ancient Egypt

(C) Howard Carter and George Herbert discovering King Tutankhamun’s
tomb, this sparked renewed interest in ancient Egypt

(D) Howard Carter and George Herbert discovering King Tutankhamun’s
tomb, they were sparking renewed interest in ancient Egypt

(E) Howard Carter and George Herbert discovered King Tutankhamun’s
tomb and sparked renewed interest in ancient Egypt

11. The professions of both psychiatrists and psychologists involve research and
diagnosis, but being unlike psychiatrists, psychologists’ professions do not
involve prescribing medications.

(A) being unlike psychiatrists, psychologists’ professions
(B) psychiatrists’ professions are unlike psychologists’ professions,
(C) psychiatrists’ professions, and unlike those of psychologists,
(D) psychiatrists’ professions, unlike those of psychologists,
(E) by being unlike psychiatrists, psychologists’ professions
12. The Foreign Legion is technically a branch of the French army, but French
citizens making up only twenty five percent of their recruits in 2007.

(A) French citizens making up only twenty-four percent of their recruits in
2007

(B) French citizens made up only twenty-four percent of its recruits in 2007
(C) French citizens making up only twenty-four percent of the total number
of recruits in 2007

(D) only twenty-four percent of their recruits being made up by French
citizens

(E) only twenty-four percent of the recruits were French citizens in 2007
13. In 1945 the International Court of Justice established its headquarters in The
Hague, Netherlands, this is a place where more than 150 international
organizations now have offices.
(A) this is a place
(B) being
(C) it being a place
(D) a place
(E) it is a place
14. Although they rarely attack humans, sharks, powerful predators that are

14. Although they rarely attack humans, sharks, powerful predators that are
capable of both severely injuring and killing if provoked.

(A) sharks, powerful predators that are capable of both
(B) sharks, which are powerful predators and capable of both
(C) sharks are powerful predators, both being capable of
(D) sharks are powerful predators and both capable of
(E) sharks are powerful predators that are capable of
15. Some trout that have been bait for striper fish once by fishermen are now no
longer used as such because they can spread damaging organisms.

(A) trout that have been bait for striper fish once by fishermen
(B) trout once used by fishermen as bait for striper fish
(C) trout, which has been used for baiting striper fish by fishermen
(D) trout, while by fishermen baiting striper fish
(E) trout, by which striper fish have been baited by fishermen
16. Citizens in large cities tend to live in smaller homes than the countryside.
(A) tend to live in smaller homes than
(B) tend to live in smaller homes than with the citizens in
(C) tend to live in smaller homes than do citizens in
(D) have tended to live in smaller homes than did
(E) tend to live in smaller homes than the homes of

17. No one will boost the chess team’s excitement like Abigail’s victory tonight.

17. No one will boost the chess team’s excitement like Abigail’s victory tonight.
(A) No one will boost the chess team’s excitement like Abigail’s victory
tonight.

(B) Nothing will boost the chess team’s excitement as much as Abigail’s
success tonight will.

(C) The excitement of the chess team will be boosted by Abigail’s success
more than any.

(D) Abigail’s success tonight will boost the chess team’s excitement like
none other.

(E) No one will boost the excitement of the chess team like Abigail’s success
will.

18. Every band that performed at the rock concert on Friday had a theft of their
guitars after the show.

(A) had a theft of their guitars
(B) had their guitars stolen
(C) that stole the guitars
(D) that had its guitars stolen
(E) had its guitars stolen
19. Many college students rarely visit the grocery store and prefer to order takeout
or eat at restaurants rather than cook meals at home.
(A) rather than cook
(B) instead of
(C) rather than cooked
(D) instead of to cook
(E) rather than

20. He was a much less famous supporter, the janitor did more to bolster the

20. He was a much less famous supporter, the janitor did more to bolster the
charity’s cause than did the well-known actress.
(A) He was a much less famous supporter
(B) Despite him being a much less famous supporter
(C) As a supporter he was much less famous
(D) While a much less famous supporter
(E) As opposed to being much less famous as a supporter

The following sentences test your ability to recognize grammar and usage errors. Each

sentence contains either a single error or no error at all. No sentence contains more
than one error. The error, if there is one, is underlined and lettered. If the sentence
contains an error, select the one underlined part that must be changed to make the

sentence correct. If the sentence is correct, select choice E. In choosing answers, follow
the requirements of standard written English.
EXAMPLE:

21.

22.

23.

23.

24.

25.

26.

27.

27.

28.

29.

30.

31.

31.

32.

33.

34.

Directions: The following passage is an early draft of an essay. Some parts of the
passage need to be rewritten.

Read the passage and select the best answers for the questions that follow. Some

questions are about particular sentences or parts of sentences and ask you to improve
sentence structure or word choice. Other questions ask you to consider organization

and development. In choosing answers, follow the requirements of standard written
English.

Questions 35-39 are based on the following passage.
(1) The Broadway play Les Miserables, based on a novel written by Victor Hugo

in 1862, has been very successful because of its musical numbers and its

captivating story. (2) The songs are very well written. (3) The play follows the

adventures of the hero Jean Valjean after he breaks parole from prison and starts a

new life. (4) The play is equally popular though because it combines action scenes,
which they all enjoy, and emotional scenes, which give the characters depth.

(5) In this play, Valjean progresses from being an escaped convict to becoming

mayor of the city of Vigo. (6) His search for redemption plays a large part in the

story. (7) For example, at one point police inspector Javert falsely accuses another
man of being Jean Valjean, and wants to put the man in prison. (8) Many men

might have been content to let an innocent person take the blame. (9) Instead of

that Valjean sought to redeem himself by stepping forward and identifying himself
as the guilty party.

(10) As a man, Valjean changes from an uncouth convict into an educated man

and finally into a caring father. (11) At first, Valjean stole and assaulted others

because he needed to eat, not because he was an evil person. (12) He simply did

what he needed to in order to survive. (13) However, as he experiences kindness
from others, he transforms into a gentle, thoughtful, and civilized man.

35. Sentence 2 (shown below) would be more effective if it began with which of

35. Sentence 2 (shown below) would be more effective if it began with which of
the following?

The songs are very well written.
(A) The play has much popular music
(B) The play containing much popular music
(C) In other words, audiences enjoy the play because
(D) It is worth noting that the play, containing a lot of popular music
(E) The musical numbers contribute to the play’s success because
36. In context, sentence 4 (shown below) requires which of the following changes?
The play is equally popular though because it combines action scenes, which they
all enjoy, and emotional scenes, which give the characters depth.
(A) Delete “though.”
(B) Change “because” to “in that.”
(C) Change “emotional” to “moving.”
(D) Delete “which give the characters depth.”
(E) Change “they all” to “audiences always.”

37. In the context of the passage, which of the following effectively revises and

37. In the context of the passage, which of the following effectively revises and
combines sentences 8 and 9 (shown below)?

Many men might have been content to let an innocent person take the blame.
Instead of that Valjean sought to redeem himself by stepping forward and
identifying himself as the guilty party.

(A) Many would have been content to let an innocent person take the

blame, but Valjean instead redeems himself by stepping forward to
identify himself as the guilty party.

(B) Many are content to let an innocent person take the blame; however

Valjean redeems himself by stepping forward to identify himself as the
guilty party.

(C) Seeking to redeem himself by stepping forward and identifying himself
as the guilty party, Valjean does what many might not have done.

(D) Redeeming himself by stepping forward to identify himself as the guilty
party was what he sought, many people would have let an innocent
person take the blame.

(E) A redeemed man was what Valjean wanted to become instead; many
others let an innocent person take the blame.

38. If the author of the passage wants to more thoroughly develop the final
paragraph, then the author should do which of the following?

(A) Refer to an authority regarding the differences between Valjean and
typical convicts of his time.

(B) Provide further details regarding the ways in which Valjean changed.
(C) Discuss the way that convicts were treated during the 1860s.
(D) Explain what Valjean did when he became mayor of Vigo.
(E) Give examples of other successful Broadway musicals.

39. Where could the author most logically add the following sentence?

39. Where could the author most logically add the following sentence?
Many plays and novels written in the 1860s feature downtrodden characters who
change their lives and achieve moral redemption.
(A) After sentence 1
(B) After sentence 3
(C) At the beginning of the second paragraph
(D) Before sentence 11
(E) At the very end of the passage

ST OP
If you finish before time is called, you may check your work on
this section only.
Do not turn to any other section in the test.

PRACTICE TEST 1 ANSWERS

You will find a detailed explanation for each question beginning on
here.

SCORING YOUR PRACTICE PSAT
Critical Reading
After you have checked your answers against the answer key, you
can calculate your score. For the two Critical Reading sections
(Sections 1 and 3), add up the number of correct answers and the
number of incorrect answers. Enter these numbers on the worksheet
on the next page. Multiply the number of incorrect answers by .25
and subtract this result from the number of correct answers. Then
round this to the nearest whole number. This is your Critical
Reading “raw score.” Next, use the conversion table to convert your
raw score to a scaled score.

Math
Calculating your Math score is a bit trickier, because some of the
questions have five answer choices (for these, the incorrect answer
deduction is .25), and some are Grid-Ins (which have no deduction
for wrong answers).
First, check your answers to all of the problem-solving questions on
Sections 2 and 4. For Section 2 and questions 21–28 of Section 4,
enter the number of correct answers and the number of incorrect
answers into the worksheet on the next page. Multiply the number of
incorrect answers by .25 and subtract this result from the number of
correct answers. For questions 29–38 of Section 4, the Grid-In
questions, simply enter the number of correct answers. Now, add up
the totals for both types of math questions to give you your total
Math raw score. Then you can use the conversion table to find your
scaled score.

Writing Skills
The Writing Skills section should be scored just like the Critical
Reading sections. Add up the number of correct answers and the
number of incorrect answers from Section 5, and enter these
numbers on the worksheet on the next page. Multiply the number of
incorrect answers by .25 and subtract this result from the number of
correct answers. Then round this to the nearest whole number. This
is your Writing Skills raw score. Next, use the conversion table to
convert your raw scores to scaled scores.

WORKSHEET FOR CALCULATING YOUR
SCORE
Click here to download a PDF of the Scoring Sheet

SCORE CONVERSION TABLE

Chapter 4
Practice Test 1: Answers and
Explanations

Section 1
1. E You know that Raquel is excited and that she pored over
cookbooks and bought utensils. She’s learning something new,
and she’s excited about it, so your missing word is going to
be positive. Eliminate choices (A) and (D). “Learning”
would be a good word to put in the blank, which makes
choice (E) the correct answer.
2. C The author wrote many different things, including poems,
short stories, and novels, so you know he has a “varied”
writing ability. Choice (C) is closest to that meaning,
making it the correct answer.
3. B The sentence tells you that the armadillo has armor-like
scales that form a shield, meaning the animal is wellprotected. The trigger although sets up a contrast between
the clue and the blank, so you need to look for a word that
is the opposite of protected. Vulnerable means exactly that,
making choice (B) the correct answer.
4. E Start with the second blank. The second part of the sentence
tells you Cecily was happy to see everyone, however the
trigger but indicates a change in direction. The second blank
will be something negative, so you can eliminate choice (C).
With a contrast set up in the second part of the sentence,
and a colon (same direction trigger) connecting the two
parts of the sentence, you know that the first blank will
mean something like “mixed.” The first blank in Choice (A)
is only positive, and choice (B) is only negative, so both of
those can be eliminated. There is no context to support her
return home being inconvenient, so you can eliminate (D).
Both bittersweet and loath fit the context of the sentence,
making choice (E) the correct answer.

5. D Start with the first blank. Because we know the winners are
large-pot winners, the missing word must mean “large
amount of money.” Eliminate choices (A), (B), and (C). For
the second blank, you know they lack the financial savvy, so
they aren’t good at dealing with money. Therefore, in a few
years, they are likely to be “broke.” Choice (D) is the
correct answer.
6. A You know that Juan demands his way and never asks anyone
else’s opinion. The rarely time trigger lets you know that you
will be looking for a word that’s the opposite of those
characteristics. Synergistic means “cooperative and working
together for a greater good,” which makes choice (A) the
correct answer.
7. D The second part of the sentence defines both of the missing
words. Recycle the words that come after the semicolon to
fill in the blanks, placing quintessential into the first blank
and professional into the second. Choice (D) is the correct
answer.
8. E Start with the first blank. Because you know the knitters are
apprehensive about the intricate patterns, but the videos will
motivate them, the videos must be clear or easy to follow.
Eliminate choices (A), (B), and (D). For the second blank, if
the videos are clear, they must “clearly explain” the tricky
stitches. That makes choice (E) the correct answer.
9. B Both authors use the “I” format.
10. D The author mentions that some may argue the films are
unrealistic or cheesy. Using unrealistic synonymously with
cheesy gives you a solid context. You can eliminate all
answers except choice (D), inauthentic, which is also
synonymous with unrealistic.

11. A The detractors mentioned in Passage 2 argue that the films
are not believable. The author of Passage 1 also feels this
way. This should lead you to look for an answer choice that
contains a positive response. Choices (B) and (E) are clearly
negative, so you can eliminate them. Choices (C) and (D)
may describe the author’s tone in Passage 1, but the
question is asking about the author’s response to the
detractors, not the author’s general tone. Choice (A) is the
correct answer.
12. D Use POE with one passage at a time. Starting with Passage
1, you can eliminate choice (A) because there’s no
comparison in Passage 1 between older and newer romantic
comedies. You can also eliminate choice (E) because there’s
no discussion of ticket prices. Now look at Passage 2 and
the second half of the answers. Choice (B) can be
eliminated because the author of Passage 2 actually quite
likes the romantic comedies, and isn’t at all fed up. Choice
(C) also doesn’t work, because the author of Passage 2
never claims to believe the films are realistic. That leaves
choice (D), which fits with both Passage 1 and Passage 2
and is the correct answer.
13. E Each sentence in the first paragraph refers to something
about the new wealth of information available. The first
sentence mentions all the information we could ever need. The
second mentions the profusion of information. Although the
author does go on to say that our approach to this
information has changed, he does not speak of it
disparagingly, as choices (A), (B), and (D) suggest.
14. A The previous generations of scholars are described as
slav[ing] away at libraries, pulling dusty books from the shelves
and hoping that those books could reveal all the world’s secrets.
This information is given in contrast to the first sentence of
the first paragraph, which shows that now that information

is all more readily available. The author does not indicate a
preference in these lines for either method, which
eliminates choices (D) and (E). And while choice (B) may be
true, the author does not state it, and it is not his main
point.
15. E The term information saturation refers back to all the
information we could ever need and the profusion of
information mentioned in the previous paragraph. The term
does not refer to scholars specifically, which eliminates
choices (A) and (D). Nor does the author suggest that
contemporary human beings are unable to learn any new
information, eliminating choice (C), only that there is too
much available information for any single human being to
know, as in choice (E).
16. D The author continually refers to the new wealth of
information as available (as in choice (D)), but he does not
indicate that we have a complete grasp or understanding of
that information, which eliminates choices (A) and (E).
Because we can still access and use some of this
information, it cannot be described as “beyond our
understanding,” as in choice (B).
17. E Pay close attention to the question. It does not ask about
“our understanding,” which might lead one to pick (A), (B),
or (C). Instead, it asks from what this understanding is a
shift away. Note the next line: where we once thought of the
‘heavens’ as the things that we could see in the sky. In other
words, the universe used to be knowable because it was
something we could see, as in choice (E).
18. E The researchers and scholar mentioned in this part of the
passage are given as examples of the older mode of study.
While they might be contrasted with newer scholars, they
are not being contrasted with newer researchers in these

lines, eliminating choice (D). Choice (B) can be eliminated
because the author is not warning against this mode of
study; he is merely describing it. Only choice (E) can work
because, while it is less specific than the others, it does not
contain any errors.
19. A Note the contrast between choices (A) and (B). These two
answers have some similarities, but choice (B) is more
extreme and should therefore be eliminated. Choice (A) is
supported in the transition between the third and fourth
paragraphs: A scholar like James Frazer, author of The
Golden Bough (1890), could be fairly certain that he was
assembling all of the world’s myths and folklore in a single
book. Now, we know that Frazer’s project was a very limited
one.
20. C Read the fourth paragraph carefully: Because we know how
much information is out there, we can’t possibly dream of trying
to assemble it all into anything as manageable as a single book.
We instead generate theories to support our impossible positions.
The author’s use of hyperbole here is used to underline the
extent to which contemporary researchers are overwhelmed
or “inundated,” as in choice (C), by the wealth of
information available.
21. E In this part of the passage, the author discusses goods from
different countries and then goes on to say that we can have
global experiences at mall food courts and that the entire world
is there for our perusal at any time of the day or night. As with
all the information that is constantly at our fingertips, so
too is the world constantly at our fingertips. This agrees
with choice (E). Choice (A) focuses too narrowly on food
courts. Choice (C) refers to consumerism as “excess,” a
value judgment that the author does not place on
consumerism. Choice (D) refers to a preference for foreign
goods, where the author refers only to their availability.

22. D The word “witchcraft” appears in the following sentence:
Just as our ancestors’ ways of life seem incomprehensibly
difficult to us, so too must ours seem impossibly large to them,
some bit of witchcraft that allows us to be everywhere at once.
Note the last part of the sentence: the witchcraft allows us to
be everywhere at once. The author is not discussing
information in this part of the essay, which eliminates
choices (A) and (E). Choice (C) refers to the older, less
international mode of consumerism. Only choice (D) agrees
with the passage.
23. E The mention of the “computer-savvy researcher” appears in
the following line: The computer-savvy researcher of today, by
contrast, can have that information instantaneously and can
even search within it for whatever bits of information seem
relevant. In other words, this researcher has an abundance
of information available to him at all times, as choice (E)
suggests.
24. B The crucial line appears at the end of the final paragraph: It
is at the very least my hope—and the hope, I suspect, of many
others—that there must be some way between the two extremes.
This “way” agrees with the “compromise” mentioned in
choice (B). The author is dismissive of neither the new nor
the old modes of research, which eliminates choices (A) and
(C). Nor is the author completely in support of the new type
of research, which eliminates choices (D) and (E).

Section 2
1. C The first step is to solve the first equation for y. To do that,
subtract 3 from each side, yielding y = 4. Now plug that
value into the second equation. This results in 2(4) + 3 =
8 + 3 = 11, so (C) is the credited response.
2. D The question asks for the greatest negative slope, so the
sides with positive slopes, AB and DE, can be eliminated.
Side BC is practically a horizontal line; it has no slope and
can also be eliminated. Of the two remaining sides, CD has
the steepest slope, making (D) the credited response.
3. D Probability is defined as the number of things that fit the
requirements divided by the total number of things. In this
case, the number of licorice sticks would be divided by the
total number of pieces of candy. This yields
reduces to

, which

. Therefore, (D) is the credited response.

4. B With variables in the answer choices, the best option is to
Plug In. Choose an easy number for b such as 4. This makes
the first equation (4 + 2)(3(4) – 6), which equals (6)(6).
Therefore z = 36. The second equation is (4 + 2)(4 – 2),
which equals (6)(2) or 12. This is the target answer. Now,
plug 36 in for z in the answer choices, trying to find the one

that equals 12. (A) is (36), which is 6, so (A) can be
eliminated. (B) is (36), which is 12, but the rest of the
answers need to be checked. (C) is (36), which equals 18,
(D) is 3(36), which equals 108, and (E) is 6(36), which
equals 216. Therefore, (C), (D), and (E) can be eliminated,
leaving (B) as the credited response.
5. E There are 360° in a plane. If three lines meet a plane to form
6 equal angles, the lines will divide the total 360° by 6,
leaving 60° per angle. Therefore, (E) is the credited
response.
6. A Each dot on the scatterplot represents one student. To find
the number of students who answered fewer questions than
expected, count the number of dots below the best fit line.
There are 8, so (A) is the credited response.
7. E Use process of elimination. The answer must include “3
times” something, so (C) can be eliminated. The expression
in the question adds 6, so eliminate (B) and (D), since they
indicate “less than.” Finally, by adding 6 after multiplying p
by 3, (A) can be eliminated, leaving (E) as the credited
response.
8. B When a question asks for a specific amount and the answer
choices are numbers, Plug in the Answers (PITA). This
question asks which number “could be” the value of t, so
start at the top instead of with the middle answer. Label the
answer choices “t,” then plug in 4 for t. The quantity 2t – 5
becomes 2(4) – 5, which is 3. This is not divisible by 4, so
(A) can be eliminated. Choice (B) is 2(5) – 5, which equals

5. This is divisible by 5, so (B) is the credited response.
With PITA, only one answer choice will work, so there is no
need to try the others.
9. C Start by marking all the information given in the problem
on the figure. If ∆ABC and ∆DEF are equilateral, then all the
long sides are 10, and AD = DB = EC = CF = 5. Because
C and D are midpoints of AB and EF, those lines are
parallel. This means that all the small triangles are also
equilateral triangles, with side lengths of 5. If each side of
quadrilateral CGDH is 5, the perimeter is 20, making (C) the
credited response.
10. A Use process of elimination on the answer choices. The first
digits are all prime numbers, so no answers can be
eliminated from that. Since the last digit of (B) is 4, which
is not prime, (B) can be eliminated. The middle digit must
be a divisor of 45, such as 5 or 9. Choice (C) has 4 in the
middle and (E) has 7, so both of those can be eliminated.
Finally, the second and fourth digits need to have 6 as their
least common multiple. Choice (D) has a 5 as the second
digit, which does not have 6 as a multiple, so the credited
response is (A).
11. D When the question asks for a specific number, use PITA.
The first step is taking half of the number, which won’t
come out evenly with odd numbers. Therefore, (A) and (C)
can be eliminated. Choice (B) is –10, half of which is –5.
Four less than that would be –9, which isn’t the original
number, so (B) is can be eliminated. Choice (D) is –8, half
of which is –4. Four less than that is –8, the original
number, so (D) is the credited response.
12. A This is a logic question, so check each answer to determine
if it helps provide more necessary information about Ringo.
(A) states that dogs that aren’t brown aren’t Labradors.

Since Ringo is not brown, this means she is not a Labrador.
Check the other answers choices to be certain (A) is the best
one. (B), (C), and (E) reveal information about some or all
brown dogs. Since Ringo is not brown, this is not useful,
and (B), (C) and (E) can be eliminated. (D) indicates that no
dogs are brown Labradors, which still does not apply to
Ringo, who is not brown, so (D) can be eliminated. (A) is
the credited response.
13. C To determine the possible number of points of intersection
between two shapes, draw them a few different ways. Move
the shapes around and try to overlap them as much as
possible. If the circle is completely within the square, there
will be no points of intersection. If the circle overlaps one
side of the square, there will be two points of intersection.
If the circle overlaps the corner of the square, there are four
points of intersection.

There is no other way to draw the two shapes that will
result in more points of intersection. Therefore, (C) is the
credited response.
14. D This question has a lot of variables, so start by plugging in
the given information. The language about the ordered pair
is confusing, but it clearly states “x = t and y = 2.” Plug
those values in to the two equations, which yields
2 = –t
2=t+n

When dealing with simultaneous equations, the best
approach is to stack them and add them together in an
attempt to make one variable disappear. When these
equations are added together, the result is 4 = n, so (D) is
the credited response.
15. B To answer this question, the number of widgets each
machine makes in one hour must be calculated. According
to the chart, Machine F makes 300 widgets in 6 hours of
operation. Divide 300 by 6 to get 50 widgets per hour for
machine F. Machine G makes 900 widgets in 15 hours of
operation. Divide 900 by 15 to get 60 widgets per hour for
machine G. To find the difference in number of widgets
made for each hour of operation, subtract 50 from 60,
which equals 10. Therefore, (B) is the credited response.
16. C When a question contains a variable, Plug In. Since 2w must
be divisible by 8, pick a number for w that will make 2w a
multiple of 8. If 2w = 8, then w = 4, which is both even
and divisible by 4. It is not divisible by 8, however, so case
III is false. Answers that contain case III can be eliminated,
so (D) and (E) are not the credited response. To determine
what “must be true,” Plug In a few more times, using some
different numbers. If 2w = 80, then w = 40, and cases I
and II are still true. If 2w = –24, then w = –12, which is
also even and divisible by 4. Therefore, (C) is the credited
response.
17. E With variables in the problem, Plugging In is the way to go.
However, these exponents are large, so simplify first.
equals q10, since division of bases means to subtract the
exponents. Now plug in something small for q, such as 2.

210 = 1,024 = s5. To solve this for s, take the fifth root of
each side, which means that s = 4. This can be plugged in
to the second equation, once it is simplified to s10. 410 =
1,048,576, the target answer. This is larger than 1,024,
which was q10, so (A), (B), and (C) are all too small and can
be eliminated. (D) is 212, which equals 4,096. This is still
too small, and (D) can be eliminated. (E) is 220, which
equals 1,048,576, the target answer, so (E) is the credited
response.
18. C When given the equation of a line in a strange format, the
first step is to manipulate the equation into the standard y
= mx + b form. For line l, which is x + 2y = 4, start by
subtracting x from each side, which yields 2y = – x + 4.
Divide both sides by 2, giving the equation for line l as y =
– x + 2. Draw a sketch of this line, with the y-intercept at
2 and a slight negative slope. Then, sketch in line m as the
reflection of line l across the x-axis. It will look something
like the following:

From the sketch, it is clear that the slope of line m will be
positive and the y-intercept will be negative. This is enough
to use POE on the answer choices. Get each one into y =
mx + b form and eliminate any choices with negative
slopes or positive y-intercepts. (A) is y =

x + 2, which

has a positive y-intercept and can be eliminated. (B) is y =
– x – 2, which has a negative slope and can be eliminated.
(C) is y = x – 2, which has the correct sign on the slope
and the y-intercept. (D) is y = –

x + 2, which is the same

as line l in the question, so it can be eliminated. (E) is y =
2x + 2, which has a positive y-intercept and can be
eliminated. (C) is the only remaining choice and is the
credited response.

19. E For a question that asks “how many” different possibilities
exist, draw a dash for each of the positions to be filled.
There are 3 digits in the code, so draw three dashes. Now
fill in each dash with the number of options possible for
that position. There are 4 even numbers less than 9: 2, 4, 6,
and 8. Therefore, the number on the first dash will be 4.
The question does not state that the numbers must be
distinct, or different, from one another. As a result, there
are also 4 options for each of the other two dashes. Now
multiply all three numbers together to get the total number
of possible codes. 4 × 4 × 4 = 64, so (E) is the credited
response.
20. B This is a very odd-looking figure, and there is no formula
for the area of such a shape. The figure could be broken
down into pieces, the area of each piece found, and the
whole thing added together. That process would be timeconsuming, so try to find a shortcut. The circle cut from the
middle of the square has the same radius as the semicircles
on the sides. If the semicircles on the left and right sides
were cut off and placed in the center of the square, they
would exactly fill that hole, as shown below.

The two remaining semicircles are centered on the sides of
the square. If each has a radius of 1, each has a diameter of
2, leaving 1 unit on each side for the radius of the arcs. This
is also the same radius as the semicircles. Each of the two
remaining semicircles could then be cut in half, creating 4
arc pieces that would exactly fill the remaining holes, as
shown below.

The whole square has been filled in and no extra pieces are
left. Therefore, the area of the shaded region is equal to the
area of the square. With a side length of 4, the area of the
square is 16, so (B) is the credited response.

Section 3
25. B The training methods are rigorous and exhausting, yet the
athletes are keeping up with the program. They must be
getting something out of it, so the results must be
“impressive.” Choice (B) is the correct answer.
26. E The styles are “different.” The colon is a same direction
trigger, so you are looking for a word that means
“different.” Choice (E) is the correct answer.
27. A

Start with the second blank. You know that the explorers
are concerned about getting lost. The second blank deals with
their fears of never returning. Because you have a change
direction trigger, but, the fears aren’t going to come true.
Eliminate choices (B), (C), and (E). Now look at the first
blank. If their fears are lessened, the maps are going to be
“really good.” Choice (A) is the correct answer.

28. D Start with the first blank. The sentence tells you that the
pufferfish produces toxins that can kill a human within 24
hours, so the missing word must mean “poisonous.”
Eliminate choices (B) and (E). In the second part of the
sentence, you have a contrast. You know the fish is really
dangerous, but there’s a description of big eyes and comically
rotund appearance, so the missing word must mean
something like “don’t accurately represent.” Choice (A) and
(C) are the opposite of what you’re looking for, but both
words in choice (D) fit the given context. Choice (D) is the
correct answer.
29. C The authors states that our ancestors had goose bumps
because they made them look more intimidating to would-be

predators but today that is no longer necessary. So replace
the blank with “something from the past.” Primitive works
well with this definition, so choice (C) is the correct answer.
30. E The author says of the others that they believed Jefferson
failed to match his actions to his strong rhetoric. This most
closely aligns with choice (E), the correct answer.
31. C The passage does mention Jefferson’s political career, but
that’s not the main point of the passage. Eliminate choice
(A). Choices (B) and (E) are mentioned briefly in the
passage, but again, are not the purpose of the passage. The
author is addressing different perspectives on the man, and
choice (C) states that. Choice (C) is the correct answer.
32. D The author states that the shoppers aren’t paying attention.
There’s nothing deliberate about their actions, so you can
eliminate choices (C) and (E). They know how the Internet
works, because they are using it, so you can eliminate
choice (B). There’s no indication that they’ve used the
wrong credit card, so you can eliminate choice (A). Choice
(D) best fits the context of the passage and is the correct
answer.
33. E The statistic is mentioned in order to show how many
people have fallen victim to identify theft. Choices (A) and
(B) are not mentioned at all. Choice (C) could be true, but
there’s no specific evidence about who those 9 million are.
Choice (D) may also be true, but specific details of the 9
million are not given. That leaves choice (E), which fits the
context of the passage and is the correct answer.
34. A Both passages discuss the recent findings of Dr. Rodney
Willoughby, so each draws upon recent findings and
theories from a medical researcher. While both passages
mention that rabies attacks the brain’s chemical makeup,

neither “describes” the brain’s chemical makeup,
eliminating choice (E).
35. B Although Passage 1 is more approving of Dr. Willoughby’s
findings, those findings are not part of Passage 1’s
discussion of the “human diploid cell rabies vaccine,”
which, according to the passage had to be administered
within six days of the patient’s contraction of the virus, before
symptoms started to appear. In Passage 2, the author states
that, Under the initial protocol, only two of the 25 treated
patients survived. Both lines suggest that rabies remains
predominantly incurable, as in choice (B).
36. B Passage 2 does address debate within the scientific
community, but the importance of that debate is not its
primary focus, eliminating choice (A). Passage 2 is critical
of the Milwaukee protocol, but not so critical as to call its
effects “deteriorating.” Only choice (B) can work, as
Passage 2 is primarily concerned with warning against a full
acceptance of the Milwaukee protocol, which remains the
subject of heated debate within the medical community.
37. C While the authors of Passage 1 and Passage 2 discuss the
same findings, the author of Passage 1 does so approvingly,
and the author of Passage 2 does so with some doubt.
Passage 2 warns against the full acceptance of the
Milwaukee protocol, so he would not fully “agree” or
“approve” of the argument in Passage 1 (eliminating
choices (A) and (E)), nor would he “dismiss” the argument,
eliminating choice (B). His attitude is more cautious, or
“skeptical,” as suggested by choice (C).
38. A The author of Passage 1 is approving of the Milwaukee
protocol, so any further evidence of the protocol’s success
would strengthen his argument. A higher survival rate in
the “25 treated patients” would certainly provide this kind

of support.
39. A The author of Passage 1 offers a hopeful message about the
Milwaukee protocol, suggesting that Jeanna’s cure gives the
medical community hope that her recovery was not merely an
outlier. The author of Passage 2 offers a more qualified
message, suggesting that Willoughby’s method remains the
subject of heated debate within the scientific community, a large
portion of which continues to believe that rabies is an incurable
disease. Only choice (A) fully captures this contrast. Passage
1 is not fantastic or amateurish, eliminating choices (B) and
(D). Passage 2 is not anecdotal or irrelevant, eliminating
choices (C) and (E).
40. C Before Naim learns about El Shorbagy (in the third
paragraph), he is frustrated with his game as described by
words and phrases like never quite as good as he wanted to
be, his biggest challenge came from his coach, characterless
devotion, and why keep playing. Choice (C) best paraphrases
these terms. The other choices use words from the passage
but are not supported by evidence from the passage, and
choice (E) is only one small part of the first two paragraphs,
in addition to the fact that it is too extreme.
41. E The word that appears in the previous sentence: if that had
been the only hurdle. This “that” and the one in the question
refer to the same thing, the competition, or the players that
Naim has to face, as choice (E) suggests. Choices (A), (C),
and (D) are all minor aspects of his difficult competition,
but the word that refers directly to the competition itself.
42. E The parentheses appear after the words to go pro, and the
words in the parentheses are as follows: his lifelong dream,
but one that seemed too hard with a unique, personalized style
of play. These lines anticipate the later discussion of
Mohamed El Shorbagy, who managed to become a pro (and

inspired Naim to do so), even with his unique style of play.
Choice (E) captures this idea most effectively. Choice (A)
does contain the word inspiration, but there is no indication
in the passage that Naim is specifically searching for that
inspiration. Choice (E) is more precise and refers to a
specific moment in the passage.
43. A This sentence appears in the following context: He loved to
watch the greats from squash history, both the English and the
Egyptian champions, and their methodical, uncannily consistent
styles of play. Naim himself wanted to be part of this great
legion of players. There is a good deal of emphasis in these
lines on greatness and champions, thus expressing Naim’s
wish to be one among these great champions, as choice (A)
suggests. Choice (B) refers only to the English style and
cannot account for the mention of Egyptian champions.
Choice (C) might be an indirect effect of becoming a great
squash player, but it is not directly mentioned in the
passage.
44. E Don’t be distracted by the word suggest. Any suggestion on
this test must have direct support in the passage, so pay
attention to the lines in question—His hope to change the
way the game was played and for his name to be known made
him think he might be better suited to the bigger stage of tennis:
where styles were not so regimented, and the best players were
like movie stars—which essentially state that Naim looked to
tennis as a sport that was both more creative and better
known, thus implying his wish to be unique and wellknown, as in choice (E).
45. E In this sentence, styles are being described as regimented. In
other parts of the passage, the traditional squash style is
described as methodical and consistent. The word regimented
must mean something similar, and choice (E) provides a
reasonable substitute. The other choices share roots or

alternate meanings with the word regimented, but they do
not work in this context.
46. A Just as Naim is considering switching to a different sport, he
discovers a new player on the pro tour who is to become the
inspiration he had been missing. The third paragraph
describes this change of heart and renewal of interest, as
choice (A) suggests. Choice (B) cannot work because there
is no indication that Naim has matured, only that he has
changed.
47. A For Naim, El Shorbagy played the traditional game, but he did
it with such flair, such incredible confidence and style, that he
seemed totally self-taught; he was almost, it seemed, expressing
his very soul as he played, the same way one might do in a
poem. Naim is therefore moved by the creativity and
personality of El Shorbagy’s game, as choice (A) states. El
Shorbagy also has popular appeal, but this is not what Naim
is so drawn to, thus eliminating choice (D).
48. D The final paragraph discusses the ways that El Shorbagy
would be a lasting influence in Naim’s life, expanding on
his initial inspiration, thus making choice (D) the best of
these answer choices. El Shorbagy does not appear until the
third paragraph, thus eliminating choices (A), (B), and (C).
Finally, even though El Shorbagy does play a traditional
game, Naim is more drawn to the non-traditional aspects of
his play, thus eliminating choice (E).

Section 4
21. D “Find the value” with numbers in the answer choices: PITA!
Start with choice (C). Plug in 3 for r (use the calculator to
be safe) and get 7,300. Too small, so eliminate choices (C),
(B), and (A) and go bigger. Plug in 4 for r and get 73,000,
which is between 8,000 and 80,000. The credited response
is (D).
22. C The figure can be trusted, so point A has coordinates of (0,
0). Since the square has a side of 8, point C has coordinates
of (–8, 8). Use the slope formula,
of line m:

, to find the slope

. Plug the answer choices into the slope

formula to get the same slope. Plug in choice (C) to get:
= –1. Alternatively, plot the answer choices to
visually see which answer makes sense. The credited
response is (C).
23. E Read The Full Question (RTFQ). The question asks for the
number of students whose GPA is less than 4.0. Since 20%
of the students scored 4.0 and greater, 80% of the students
scored less than 4.0. Take 80% of the 30,000 students,
(30,0000 × 0.80), to get 24,000 students. The credited
response is (E).
24. C Don’t get fancy. Just write out the pattern. 1st is 1 × 3 = 3.
2nd is 3 × 5 = 15. 3rd is 5 × 7 = 35. 4th is 7 × 9 = 63.

5th is 9 × 11 = 99. 6th is 11 × 13 = 143. 7th is 13 × 15
= 195. 8th is 15 × 17 = 255. The question asked for the
difference between the 7th and 8th term, so subtract: 255 –
195 = 60. The credited response is (C).
25. C Variables in the answer choices: Plug In! In this case the
problem provides the numbers to plug in. The correct
expression will work for both situations. Using choice (C),
plug in the number of miles Gilbert drove the car for m and
check the result against his total charge. First plug in the
numbers for Monday. He drove 20 miles, so (.25)(20) + 8
= 13, which matches Gilbert’s charge of $13. Now plug in
the numbers for Friday. He drove 14 miles, so (.25)(14) +
8 = 11.50, which matches Gilbert’s charge of $11.50. Since
both situations check out, the credited response is (C).
26. C “Find the value” with numbers in the answer choices: PITA!
The question asks for the value of b, which is the x value in
the function. Start with choice (C). So g(7) = 33 – 4(7) =
5, which matches the target of 5. The credited response is
(C).
27. A Be careful: the figure is not drawn to scale and will need to
be redrawn. Two properties of triangles are needed to
answer this question. First, the largest side is opposite the
largest angle and the smallest side is opposite the smallest
angle. Second, the third side of a triangle must be less than
the sum of the other two sides and greater than the
difference of the other two sides. Since AB = 200 and BC
= 5, (200 – 5) < AC < (200 + 5). Therefore 195 < AC <
205. If the triangle is drawn so that AC = 196, then AB is
the largest side, BC is the smallest side, and AC is in
between. Therefore r < s < t, which eliminates choices (B),
(D), and (E). But if the triangle is drawn so that AC = 204,
then AC is the largest side, BC is the smallest side, and AB is
in the middle. Therefore r < t < s, which eliminates choice

(C). The credited response is (A).
28. E There are two ratios given, both of which contain “medium
shirts.” Use the ratio box to find the overall ratio of small to
medium to large.

Use the medium column to find that the multiplier is 3. Fill
in the multiplier and find the value for small.

The question asks for is the ratio of small shirts to all other
shirts, so that’s 15:(6 + 5) which is 15:11. The credited
response is (E).
29. 51 Take it in bite-sized pieces. The 8 salesmen each sold 5 cars,
so 8 × 5 = 40 cars. Then 3 of the salesmen each sold 3
more cars, so 3 × 3 = 9 more cars. Then 2 salesmen each
sold 1 more car, so 2 × 1 = 2 more cars. Add them all
together to get a total of 40 + 9 + 2 = 51 total cars sold.
30. 2,018 First, it might be easier to convert the feet to inches.
There are 12 inches in a foot, so 230 feet is 2,760 inches
and 235 feet is 2,820 inches. Therefore the distance in 1976
is 2,760 inches and in 1983 is 2,823 inches. Then find the
rate. The difference between 1983 and 1976 is 7 years and
the difference between 2,823 inches and 2,760 inches is 63

inches. At this rate, the distance will increase 63 inches
every 7 years. The simplest way to continue is to add the
rate until you reach 261.5 feet, which is 3,138 inches. For
example, starting from 1983, add 7 years to get 1990 and
add 63 inches to get 2,886 inches. Continue that pattern. In
1997 the distance is 2,949 inches. In 2004 the distance is
3,012 inches. In 2011, the distance is 3,075 inches. In 2018,
the distance is 3,138 inches.
31. 10 Since all of the angles are right angles, the figure can be cut
up into a bunch of rectangles. The horizontal base is 15, so
the sum of the other horizontal pieces must also equal 15.
Solve 9 + 2 + x = 15 to find that x = 4. Now, the vertical
side labeled 3x must equal 12. The vertical height on the left is
25, so the sum of the vertical heights on the right must also
equal 25. Solve 12 + 3 + z = 25 to find that z = 10.
32. 28.5 Vertical angles are equal and x = 123, so ∠AEB = 123.
ABCD is a rectangle, so the diagonals are the same length
and intersect at each other’s midpoint, making AE = BE.
Therefore ABE is an isosceles triangle and y = z. The sum
of all the angles in a triangle is 180°, so y + z + 123 =
180. Solve the equation to find that y + z = 57. Since y =
z, substitute to find that z + z = 57. Solve to find that 2z
= 57, so z = 28.5.
33.

2.5 or
A quadratic equation is symmetrical. Draw a vertical line
down the center of the curve, which should pass through its
lowest point. The points to the left and the right will be the
same distance from the vertical line, so the line will be

halfway between two points with the same y value. The two
points given have the same y value, so the vertical line will
be halfway between –1 and 6. To find the halfway point,
take the average of –1 and 6:

= 2.5. Therefore,

the vertical line is x = 2.5, which is the x-coordinate of the
lowest point (least value) of the function.
34.

4, 9, 24
Put the numbers in order: 1, 8, 12, 15. But where to place
the unknown fifth number? It could go above the median,
below the median, or it could be the median. Do one of the
following.
If the fifth test score is placed above the median then the
list is now 1, 8, 12, 15, x, which makes the median of the
list 12. The median is equal to the mean, so the mean is also
12. Use the average pie to solve for x. The number of things
is 5 and the average is 12. Multiply to find that the sum of
the test equals 60. Therefore 1 + 8 + 12 + 15 + x = 60
and x = 24.
If the fifth test score is placed below the median then the
list is now x, 1, 8, 12, 15, which makes the median of the
list 8. The median is equal to the mean, so the mean is also
8. Use the average pie to solve for x. The number of things
is 5 and the average is 8. Multiply to find that the sum of
the test equals 40. Therefore 1 + 8 + 12 + 15 + x = 40
and x = 4.
If the fifth test score is the median then the list is now 1, 8,
x, 12, 15, which makes the median of the list x. The median

is equal to the mean, so the mean is also x. Use the average
pie to solve for x. The number of things is 5 and the average
is x. Multiply to find that the sum of the test equals 5x.
Therefore 1 + 8 + 12 + 15 + x = 5x so 4x = 36 and x
= 9.
35. 15 Don’t worry about the markings on the number line. The
two points are given and the distance between them is
known. Set those equal to each other. The difference
between the two points equals the distance, so 0.8x – 0.6x
= 3, then 0.2x = 3, and x = 15.
36. 1,996 500 numbers are too many to write out, so pick an easy
number to start with and then extrapolate. The easiest
number to start with is the first multiple of 4, so the first
number in the list is 4 × 1 = 4. The second number in the
list is 4 × 2 = 8. Using this pattern, the five hundredth
number in the list is 4 × 500 = 2,000. Subtracting the
smallest from the largest results in 2,000 – 4 = 1,996.
37. 1,280 Write down the volume formula: v = l × w × h. The key
to this question is to find the dimensions inside the box. The
board on the top right is labeled with a length of 12 inches,
but it is overlapped by the board on the right. The overlap
is 4 inches, so the length inside the box is 8 inches. The
inside width is also 8 inches for the same reason. The height
of each board is 2 inches. The boards are stacked 10 high,
so the total height is 2 × 10 = 20 inches. Use the volume
formula to solve. 8 × 8 × 20 = 1,280.
38.

2.5 <

<3

The question looks more complicated than it is. It is not
necessary to solve for x to answer this question. RTFQ and

look for similarities. The question contains
goal is
Notice that

and the

. What is the relationship between them?
is half of

. Therefore, divide all

sides of the inequality by 2 to find that 2.5 <
Choose any number in that range, for example 2.8.

< 3.

Section 5
1. B The pronoun it is singular, but refers to ankles, which are
plural. Therefore, this sentence contains a pronoun
agreement error. Eliminate choices (A) and (C), which both
use it. Introducing either the word when or the word by
turns the sentence into a fragment, so choices (D) and (E)
are also incorrect. Choice (B) fixes the pronoun agreement
error and makes the sentence complete, so choice (B) is the
correct answer.
2. E The word while suggests that this sentence contains a
contrast. However, since the sentence does not introduce
another contrasting thought at the end of the phrase, this
sentence is currently a fragment. Therefore, you can
eliminate choice (A). Choice (D) repeats this error by using
although, which is also a contrast word, so you can
eliminate choice (D). Choice (B) uses because, which
similarly makes the sentence incomplete. Choice (C) uses
the word being. In general, avoid choosing an answer that
uses the word being whenever possible. Therefore, choice
(E) is the correct answer.
3. A Having swum may sound odd, but the phrase contains the
correct verb tense. Therefore, keep choice (A) for now.
Choice (B) uses she immediately after Diana Nyad, and
therefore contains a redundancy error. Choice (C)
incorrectly uses so, and is therefore incorrect. Use a comma
and select conjunctions—For And Nor But Or Yet So
(FANBOYS)—to join two complete thoughts. Since the
phrase Diana Nyad having swum from Cuba to the United
States is not a complete thought, you cannot use a comma
and a conjunction to join this phrase to the rest of the

sentence. Therefore, choice (D) is not the credited answer.
Choice (E) changes the intended meaning of the sentence,
and is incorrect. Since choice (A) does not contain any
grammatical errors, it is the correct answer.
4. C The phrase much less expensive in cost is redundant, since less
expensive already refers to cost. Therefore, you can eliminate
choice (A). Using reason with because is also redundant, so
you can eliminate choice (B). Choice (C) does not contain
any redundancies or introduce any new errors, and is the
correct answer. Both choices (D) and (E) incorrectly use the
word being. If possible, avoid choosing answers that contain
being.
5. C The clause In 1958 Chinua Achebe attempted to print his novel
Things Fall Apart, sending the manuscript to several publishers
is a complete thought. The clause some of them rejected it
immediately is also a complete thought. Therefore, this
sentence contains a comma splice. Choice (E) repeats this
error, so eliminate choices (A) and (E). Choice (B)
unnecessarily uses that and is therefore not as concise as
choice (C). Choice (D) uses which, rather than whom. Since
the pronoun refers to publishers, who are people rather than
things, you want to use whom. The correct answer is
therefore choice (C).
6. E Use more to compare two things, but use most to compare
more than two things. Since this sentence compares many
works of art and the Mona Lisa, you need most rather than
more. Eliminate choices (A), (B), and (D). Choice (C)
incorrectly uses plus and is therefore not the credited
answer. Choice (E) fixes the original error and does not
introduce any new errors, so it is the correct answer.
7. A Choice (B) incorrectly uses being and is therefore incorrect.
Choice (C) uses hindered … to. Since the correct idiom is

hindered from, this choice is incorrect. Choice (D) repeats
the idiom error because it does not contain a preposition at
all. Choice (E) changes the verb from active voice to passive
voice, and is therefore incorrect. Choice (A) does not
contain any grammatical errors and is therefore correct.
8. E The phrase In 1783, while only thirteen years old is a
modifying phrase and must describe whatever comes after
the comma. Since Beethoven, and not the piano sonatas,
was thirteen years old, then Beethoven must come
immediately after the comma. Choices (A), (B), and (C)
repeat the original error and are therefore incorrect. Choice
(D) contains two complete thoughts joined by a comma,
and is therefore a comma splice. Choice (E) fixes the error
in the original sentence, and does not contain a comma
splice. Therefore, the correct answer is choice (E).
9. B The verb had … completed is in the past perfect tense. To
correctly use the past perfect tense, you must be referring to
a past event that occurred before some other past event.
Since you do not have two separate past events in this
sentence, the verb had completed is incorrect. Eliminate
choice (A). The verb could complete does not agree with will
be, which is in the future tense. Therefore, eliminate choices
(C) and (E). The verb can complete also does not agree with
the future tense verb will be, so choice (D) is also incorrect.
Choice (B) fixes the original error in the sentence, and does
not introduce any new verbs, so it is the correct answer.
10. E The phrase After digging for several years is a modifying
phrase that must describe whatever appears right after the
comma. Since Howard Carter and George Herbert, not the
discovery, dug for several years, you need Howard Carter and
George Herbert to come immediately after the comma.
Eliminate choices (A) and (B). Choices (C) and (D)
incorrectly use discovering rather than discovered. The

correct answer is therefore choice (E).
11. D This sentence incorrectly compares psychiatrists to
psychologists’ professions. Since you want to compare
professions to other professions, rather than people to
professions, eliminate choice (A). Choice (E) repeats the
original comparison error and is therefore incorrect. Choice
(B) uses the verb are, which makes the phrase do not involve
prescribing medications into a fragment. Choice (C) correctly
compares psychiatrists’ professions and those of psychologists,
but uses the same direction conjunction and to link the two.
However, since the sentence is discussing a contrast, rather
than a similarity, and is not the correct conjunction to use
here. Eliminate choice (C). Choice (D) fixes the original
error by using those of to refer to the professions of
psychiatrists and is therefore the correct answer.
12. B This sentence contains a parallelism error, since The Foreign
Legion is is not parallel with French citizens making.
Therefore, you can eliminate choices (A) and (C), both of
which use making. Choice (D) uses being, and is also
incorrect. Choice (E) changes the meaning slightly by
suggesting that the people who were recruits were simply
not French citizens in 2007, but might be French citizens
now. It also incorrectly uses the definite article the, when
there are no specific recruits involved. Choice (B) fixes the
parallelism error and retains the original meaning of the
sentence, and is therefore the correct answer.
13. D The clause In 1945 the International Court of Justice
established its headquarters in The Hague, Netherlands is a
complete thought. The clause this is a place where more than
150 international organizations now have offices is also a
complete thought. Since only a comma divides these two
thoughts, this sentence contains a comma splice. Choices
(A) and (E) repeat the original error, and are incorrect.

Choices (B) and (C) use being. If possible, avoid choosing
grammar answers that use the word being. Therefore, you
can eliminate choices (B) and (C). Choice (D) fixes the
original error and does not introduce any new errors, so it is
the correct answer.
14. E The phrase Although they rarely attack humans is an
incomplete thought. Since the phrase sharks, powerful
predators that are capable of both severely injuring and killing if
provoked is also an incomplete thought, this sentence is a
fragment. Choices (A) and (B) repeat the original error.
Choice (C) uses being, and if possible, you want to avoid
choosing grammar answers that use being. The phrase are
capable of severely injuring and killing if provoked describes
sharks, and is not a new, separate thought, so you want to
use that rather than and. Therefore, choice (E) is the correct
answer.
15. B This sentence is missing a verb, since you cannot describe
trout as bait, but rather must say that they have been used
as bait. Therefore, choice (A) is incorrect. Choice (B) fixes
the error by introducing the verb used. In order to maintain
the original meaning of the sentence, by fisherman should
come before, rather than after striper fish. Therefore you can
eliminate choices (C) and (E). Note that choice (C) also uses
the singular verb has to refer to trout, while the nonunderlined portion uses the plural verb are. Choice (D)
turns the sentence into a fragment and is therefore
incorrect. The correct answer is choice (B).
16. C This sentence compares citizens in large cities to the
countryside. Since you want to compare citizens to other
citizens, not to areas, this sentence contains a comparison
error. Choices (A), (D), and (E) repeat this error. Since the
sentence needs to compare the homes in which one group
lives to the homes in which another group lives, the

sentence needs to include verbs in both parts of the
comparison. Choice (B) incorrectly uses with, rather than
do, and is therefore not the credited answer. Choice (C)
fixes the comparison error by phrasing the sentence so that
it compares the homes in which citizens in large cities live
to homes in which citizens in the countryside live. Choice
(C) is the correct answer.
17. B As the sentence is currently written, it compares No one, or
a person, to Abigail’s victory, or a thing. Since you must
compare people to people and things to things, this
sentence contains a comparison error. Choices (A) and (E)
repeat the original error. Choice (C) uses the passive phrase
will be boosted and also contains the phrase more than any,
which does not directly refer to anything else in the
sentence. Choice (D) changes the intended meaning of the
sentence by suggesting that no other success will boost the
chess team’s excitement as much as Abigail’s success will,
while the original sentence suggests that nothing else at all
will boost the chess team’s excitement as much as Abigail’s
success will. Choice (B) is therefore the correct answer.
18. E This sentence uses the plural pronoun their to refer to the
noun band, which is singular, so this sentence contains a
pronoun agreement error. Choices (A) and (B) repeat the
original error. Choice (C) changes the intended meaning of
the sentence by suggesting that the band stole the guitars,
rather than that the band’s guitars were stolen. Choice (D)
uses that, which turns the sentence into an incomplete
thought. Therefore, the correct answer is choice (E).
19. A This sentence correctly contrasts two things that college
students do: they prefer to order take out rather than to
cook. Since the sentence contrasts two actions, it does not
contain a comparison error. However, choices (B) and (E)
contrast an action (preferring to order take out) and a noun

(meals at home). Therefore, these two choices are incorrect.
Choice (C) incorrectly changes the verb to past tense, and is
therefore not the credited answer. Choice (D) incorrectly
changes the comparison word to instead, and unnecessarily
adds the word to. Since the original sentence is correct as
written and is more concise, choice (A) is the correct
answer.
20. D The clause He was a much less famous supporter is a complete
thought. Since the clause the janitor did more to bolster the
charity’s cause than did the well-known actress is also a
complete thought, this sentence contains a comma splice.
Choices (A) and (C) repeat the original error. Choices (B)
and (E) both use the word being, and if possible you want to
avoid choosing answers that use being. Choice (D) fixes the
error in the original sentence and does not introduce any
new errors, so it is the correct answer.
21. B The verb in the non-underlined portion of the sentence is
majored, which is in the past tense. Therefore, is attending,
which refers to an action occurring in the present, is not in
the correct tense. The verb should be attended.
22. A This sentence incorrectly refers to the two men Meriwether
Lewis and William Clark as a frontiersman. Since a
frontiersman is singular, it cannot refer to two individuals.
This sentence contains a noun agreement error.
23. B In this sentence the word indicating is in the wrong verb
form because it creates a fragment. In order to be complete,
the sentence should use the verb indicate.
24. D Choice (D) uses the singular verb directs. However, the
subject of the sentence is conductors, which is plural.
Therefore, this sentence contains a subject-verb agreement
error, and choice (D) is the credited answer.

25. A If you use the word either in a sentence, you must also
include the word or later in the sentence. Since this
sentence uses and instead, the use of the word either is
incorrect. Use both if you are referring to one thing and
another.
26. E The pronoun there must refer to a place, and in this case it
correctly refers to the hotel. Therefore, choice (A) does not
contain an error. Choice (B) contains the singular verb
overbooks. Since the subject of the verb is staff, which is also
singular, this choice does not contain a subject verb
agreement error. Nothing in the sentence indicates that the
verb should be in a different tense, so there are no tense
errors, and the verb is not in a list, so there are no
parallelism errors. Choice (B) is therefore error-free. Choice
(C) correctly uses the singular pronouns his and her to refer
to everyone, which is also singular, so choice (C) does not
contain an error. Choice (D) contains a verb in the correct
tense, and does not contain any subject-verb agreement
errors. Additionally, driving to is the correct idiom, so choice
(D) does not contain any errors. The correct answer is
therefore choice (E).
27. C Choice (C) contains the plural verb have become. Since the
subject of that verb is cheating, which is singular, choice (C)
contains an error. Use the singular verb has, rather than the
plural verb have, with singular subjects.
28. A This sentence compares the situation with Bill and the
pronoun I. You can compare situations to situations and
people to people, but you cannot compare situations to
people. Therefore, choice (A) contains a comparison error.
29. C This sentence lists two things that the new employees have
been doing: they have been working overtime and they arrive
early to work each day. However, remember that items in a

list should be parallel. Thus, the verbs have been working
and arrive should be in the same form. Since working is not
underlined, arrive must be the verb that is in the incorrect
tense. Therefore, choice (C) contains an error and is the
correct answer.
30. A The phrase Riding in an airplane for the first time is a
modifying phrase that should describe whatever appears
immediately after the comma. Liam is the person who is
riding the in the airplane, but his name does not appear
immediately after the comma. Since the part of the sentence
that comes right after the comma is not underlined, you
cannot change that part of the sentence. Therefore, the
error must be in the modifying phrase itself. Changing the
phrase to When he rode in an airplane would fix the problem
by using the pronoun he to ensure that the phrase refers to
Liam instead of there were too many pockets of turbulence.
31. C Here, the adjective inexpensive modifies the verb can be
purchased. However, you must use adverbs, rather than
adjectives, to modify verbs. Thus, inexpensive should be
changed to inexpensively, and the correct answer is choice
(C).
32. B The word suppose means to think. However, supposed means
required. Since this sentence refers to something the author
was required to do, rather than something that he or she
thought, choice (B), which uses suppose, contains a diction
error.
33. E Choice (A) contains the phrase in the hallway. The word in is
the correct preposition to describe something inside the
hallway. The article the refers to the singular specific noun
hallway, and is therefore correct. The noun hallway is
singular, and does not have any agreement problems with
verbs or other nouns in the sentence. Therefore, choice (A)

does not contain an error. The verb lie is in the present
tense, and since the books are currently on the table, the
verb is in the correct tense. The subject of the plural verb lie
is the plural noun books, so this subject and verb agree. The
verb lie is not in a list of things, so there are no parallelism
errors. Therefore, choice (B) does not contain an error. The
verb borrowed is in the past tense, and since the act of
borrowing occurred last month, the past tense is
appropriate. The subject I agrees with the verb borrowed, so
there are no subject verb agreement errors in choice (C).
Finally, the verb borrowed is not in a list of things, so there
are no parallelism errors in this choice. Therefore, choice
(C) is correct as written. The adverb yet in choice (D)
modifies the verb returned, so the adverb is correctly used.
Finally, the verb have not…returned is in the correct tense,
and agrees with the subject I. Therefore, choice (D) does not
contain an error. This sentence is correct as written, so the
correct answer is choice (E).
34. B The singular verb appears does not agree with the plural
openings. Therefore, choice (B) contains a subject-verb
agreement error.
35. E The previous sentence describes two reasons for the play’s
success: it has been very successful because of its musical
numbers and its captivating story. Therefore, in order to
transition from the reasons for its success into a discussion
of the music, the next sentence should relate the play’s
songs to the play’s success. Choice (A) contains a complete
thought, and since the original sentence also contains a
complete thought, joining the two would create a run-on.
Choice (B) uses the incorrect verb form containing. Choice
(C) is grammatically acceptable, but the phrase In other
words suggests that what follows should simply restate the
previous sentence. However, since that is not the case,

choice (C) is incorrect. Choice (D) contains two fragments,
which, if joined with the original sentence, would not
create a complete thought. Choice (E) relates the previous
sentence, which discusses the fact that the play’s music is
one reason for its success, to sentence 2, which discusses
the fact that the music is well written. Therefore, choice (E)
is the correct answer.
36. E The word though correctly refers to a contrast between the
thoughts presented in sentence 3, which discusses the play’s
music, and the thoughts presented in sentence 4, which
discusses the nature of the play’s scenes. Therefore, you can
eliminate choice (A). The phrase in that is not a
conjunction, so you would not want to use it to replace the
conjunction because, which is correctly used in the sentence.
Therefore, you can eliminate choice (B). Changing emotional
to moving does not significantly alter the meaning or the
grammar of the sentence, so the sentence does not require
this change. Therefore, you can eliminate choice (C). If you
deleted the phrase which give the characters depth, the
sentence would still be grammatically correct. However, the
sentence does not require this change, since the phrase is
correctly used. Therefore, you can eliminate choice (D). The
pronoun they does not clearly refer to anyone in the
sentence, and is therefore ambiguous. Replacing they all
with audiences always would fix this error. Therefore, choice
(E) is the correct answer.
37. A Choice (A) correctly links the two sentences and does not
introduce any new errors. Choice (B), however, changes the
verb would have been to are. Since the sentence discusses a
hypothetical situation and not one that is actually
occurring, are is incorrect. Choice (E) similarly uses the
present tense verb let, which would also refer to a real
rather than a hypothetical situation. Therefore you can

eliminate choice (E). Choice (C) combines the two
sentences, but uses many –ing verbs. If you have a choice
between an answer that uses many –ing verbs and one that
does not, you should choose the answer that does not
contain as many –ing verbs. Therefore, choice (A) is more
effective than choice (C). Finally, choice (D) contains two
complete thoughts joined by a comma, and is therefore a
comma splice. It is also in the passive voice. The correct
answer is choice (A).
38. B The final paragraph focuses on the ways in which Valjean
changes, so the correct answer should refer to this topic.
Since the passage never discusses ways in which Valjean
differs from other convicts of his time, the author does not
need to refer to an authority on this matter. Choice (A) is
therefore incorrect. Choice (B) refers to the ways in which
Valjean changes throughout the story, and is therefore the
correct answer. The final paragraph does discuss the fact
that Valjean was a convict, but the way that he was treated
during that time is not the focus of the paragraph, so you
can eliminate choice (C). Paragraph two, not paragraph
three, refers to Valjean’s time as a mayor, so this topic
would be out of place in paragraph three. Choice (D) is thus
incorrect. Broadway musicals are mentioned in the first
paragraph, not the third paragraph. Therefore, this topic
would be out of place in paragraph three. The correct
answer is choice (B).
39. C Sentence 1 does discuss the fact that Les Miserables is a play
based on a novel that was written in the 1860s. However,
nothing in sentence 1 or the sentence that follows discusses
downtrodden characters who change their lives and seek to
achieve moral redemption. The next sentence discusses the
play’s music, so placing the new sentence after sentence 1
would not create a smooth transition between the two.

Sentence 3 discusses the play’s topic, and sentence 4 refers
to the fact that the play is popular because of the types of
scenes it portrays. Since neither of these thoughts is related
to plays and novels of the 1860s in general or to
downtrodden characters who change their lives, choice (B)
is incorrect. Paragraph one discusses the fact that Les
Miserables is a play written in the 1860s, and paragraph two
focuses on the ways in which Valjean changes and searches
for redemption, so placing the new sentence at the
beginning of paragraph two would serve to link the two
paragraphs. Sentence 10 discusses the fact that Valjean
changes throughout the story, but sentence 11 contains
information about the reasons that Valjean acted as he did.
Information regarding plays and novels of the 1860s would
be irrelevant to either of these sentences, so this choice is
incorrect. The final paragraph focuses on the ways that
Valjean changes throughout the story, but does not discuss
plays and novels of the 1860s in general. The new sentence
contains information unrelated to the rest of the paragraph,
so choice (E) is not the credited answer. The correct answer
is choice (C).

Part III
Drills

Chapter 5
Drills

SECTION 1
Time — 25 minutes
24 Questions
(1-24)
Directions: For each question in this section, select the best answer from among the
choices given and fill in the corresponding circle on the answer sheet.

Each sentence below has one or two blanks, each blank indicating that something has
been omitted. Beneath the sentence are five words or sets of words labeled A through
E. Choose the word or set of words that, when inserted in the sentence, best fits the
meaning of the sentence as a whole.
Example:

Desiring to ------- his taunting friends, Mitch gave them taffy in hopes it would keep
their mouths shut.

(A) eliminate (B) satisfy (C) overcome (D) ridicule (E) silence

1. Those who were leaving for the holiday were excited to ------- the campus,
since the semester had been both challenging and stressful.

(A) reenter (B) vacate (C) weaken (D) initiate (E) resume
2. The fact that Henry had earned a position as a starter on the varsity basketball
team made him the ------- of his less ------- second-string teammates who were
jealous of his success.

(A) pleasure . . motivated
(B) rival . . studious
(C) symbol . . coordinated
(D) mystery . . motivated
(E) envy . . athletic

3. Already one of the most famous scientists in the world, Albert Einstein

continued to ------- scientific ------- when he won the Nobel Prize for Physics in
1921.

(A) earn . . apathy
(B) ignore . . derision
(C) establish . . accolades
(D) disdain . . notoriety
(E) garner . . acclaim
4. The black mamba snake’s lethality, evident in its high toxin levels, quick

strikes, and aggressive unpredictability, presents a fearsome example of -------.
(A) vagrancy (B) agility (C) virulence (D) agitation (E) destruction

5. The reviewer denounced the actress’s ------- style: her flat performance reduced
the well-written script to a tedious recitation.

(A) brusque (B) sanctioned (C) arbitrary (D) dramatic (E) monotonous
6. The Senate majority voted to change the chamber’s rules on -------, on speaking
at inordinate length to obstruct a legislative assembly.

(A) filibustering (B) vetoing (C) oppression (D) falsification
(E) initiating

7. The chance that a wide-reaching enterprise will ------- consumers increases

7. The chance that a wide-reaching enterprise will ------- consumers increases
when the enterprise has a monopoly on a market; thus ------- is highly
beneficial.

(A) exploit . . competition
(B) manipulate . . vitality
(C) capitalize . . allocation
(D) assist . . opposition
(E) sustain . . coercion
8. Since a vast majority of the bacteria on the human body are advantageous to

their host, a tricky question is how to distinguish the few pathogens that are ------ from the preponderance that are -------.
(A) allies . . beneficial
(B) invaders . . contaminated
(C) menaces . . propitious
(D) parasites . . noxious
(E) portents . . hardy

The passages below are followed by questions based on their content; questions

following a pair of related passages may also be based on the relationship between the

paired passages. Answer the questions on the basis of what is stated or implied in the
passage and in any introductory material that may be provided.

Questions 9-12 are based on the following passages.

9. Both Locke and Hebb suggest that environmental factors are

9. Both Locke and Hebb suggest that environmental factors are
(A) crucial for tabula rasa
(B) interwoven with genetic traits
(C) subject to government regulations
(D) secondary to hereditary factors
(E) influential to human development
10. Hebb uses the geometry analogy (lines 16-18) in order to suggest that “nature”
is

(A) easily understood through a formula
(B) less understood by psychologists
(C) a combination of hereditary and environmental factors
(D) inseparable from “nurture”
(E) of little benefit to anyone other than anthropologists
11. Passage 1 suggests that Locke would most likely respond to what Hebb says
(lines 24-26, Passage 2) by

(A) pointing out that twins with similar genetic material have different
characteristics

(B) criticizing Hebb for not defining “nature” and “nurture”
(C) restating his belief that humans do not have innate rules for processing
information

(D) arguing that Hebb’s analogy is too broad for the topic
(E) denying that the question is relevant for modern scientists

12. Which best describes the relationship between Passage 1 and Passage 2?

12. Which best describes the relationship between Passage 1 and Passage 2?
(A) Passage 2 offers a scientific perspective on a theory outlined in Passage
1.

(B) Passage 2 contradicts a modern assumption made in Passage 1.
(C) Passage 2 presents a contemporary analysis of a theory stated in Passage
1.

(D) Passage 2 synthesizes two disparate views presented in Passage 1.
(E) Passage 2 explores a solution to a problem described in Passage 1.

Questions 13-24 are based on the following passage.
In this passage, a literary critic discusses some of the issues he encountered while

researching the life of Jean Toomer (1894-1967), an author from the early to mid-

twentieth century. Most famous as the author of the seminal book Cane (1923), Toomer
was also a deeply private individual, whose views of race were often in conflict with
those of others from his time.

13. The author suggests that Toomer’s relationship with the black community “has

13. The author suggests that Toomer’s relationship with the black community “has
remained a mystery to literary historians” (lines 2-3) because

(A) details of Toomer’s later life are insufficient to explain his personal
attitudes

(B) Toomer’s literary reputation was dismissed by many of his
contemporaries

(C) Toomer’s fame in literary circles was not acknowledged by white
authors

(D) Toomer’s essays provide inconsistent representations of his views
(E) evidence shows that Toomer worked against the Civil Rights movement
14. In lines 1-33, the author’s discussion of Toomer’s contemporaries and later
artists is used to

(A) show how one particular era viewed the role of race in art
(B) state that Toomer lived in an era of radical social change
(C) give evidence of their views of Toomer’s influence on black artists and
thinkers

(D) provide examples of Toomer’s literary mastery and experimentation
(E) list the challenges faced by black artists in contemporary society
15. In line 9, “unreserved” most nearly means
(A) vacant
(B) disrespectful
(C) available
(D) garrulous
(E) complete

16. The author mentions Waldo Frank and Sherwood Anderson (lines 14-15) as

16. The author mentions Waldo Frank and Sherwood Anderson (lines 14-15) as
indications of the

(A) urgency with which Toomer courted a white readership
(B) fluctuating reputation Toomer had within the black community
(C) limited supply of published reviews of Toomer’s first novel
(D) types of influences upon which Toomer drew in writing Cane
(E) appeal that Toomer had to both black and white readers
17. The author most directly supports the statement in lines 20-21 (“For
many … inspiration”) by citing

(A) influences from which Toomer drew inspiration
(B) the reception of Toomer’s work by contemporary black critics
(C) lists of Toomer’s most famous published works
(D) aspects of Toomer’s art that showed a new way
(E) ways that Toomer’s art addressed racial issues
18. In line 46, “These scraps” most directly refers to evidence that
(A) gives actual details of Toomer’s biography
(B) paints a complete picture of Toomer’s life
(C) frees literary historians to speculate
(D) reaffirms the messages found in Toomer’s work
(E) depicts the state of contemporary race relations

19. In lines 48-57, the author discusses “race activism” (line 48) primarily to

19. In lines 48-57, the author discusses “race activism” (line 48) primarily to
(A) demonstrate that Toomer’s racial attitudes were atypical
(B) praise the achievements of the Civil Rights movement
(C) refer to a major equality movement in American history
(D) give literary historians one reliable source of biographical information
(E) state that Toomer had no interest in contemporary race relations
20. In line 55, “taken” most directly emphasizes which aspect of Toomer’s
approach to race issues?

(A) His disapproval of broad social changes
(B) His ability to play both sides of an issue
(C) His focus on smaller matters
(D) His eagerness to fight for broader causes
(E) His reputation as a literary artist
21. In lines 58-69, the author emphasizes which point about Toomer?
(A) His contemporaries disparaged him for his cowering attitude toward
social equality.

(B) His attitude toward race was rooted in private and philosophical
concerns.

(C) His public attitude toward race differed sharply from his private views.
(D) His writings on race have a tendency to mislead literary historians.
(E) His commitment to racial equality influenced his political views on race.

22. In line 63, “black and white” most nearly means

22. In line 63, “black and white” most nearly means
(A) faintly tinged
(B) socially progressive
(C) racially complex
(D) hopelessly confused
(E) reductively simple
23. Which resource, if it existed, would be most helpful for the task described in
lines 72-75 (“Unfortunately … artist”)?

(A) Accurate information about the progress of social equality in the United
States

(B) Toomer’s personal diary or autobiography
(C) Records of household income kept by Toomer’s wives
(D) Writings by other black authors from the 1920s
(E) Statements from later authors about the importance of Toomer’s
influence

24. The final phrase in lines 77-79 (“if … own”) primarily emphasizes which of
the following points?

(A) Toomer hid the details of his race from those in his family and
hometown.

(B) Toomer identified as white at the end of his life to distance himself from
Civil Rights.

(C) Those in the Civil Rights movement were correct to dismiss Toomer as a
counterproductive force.

(D) Toomer had more advanced views than most African American authors
from the 1920s.

(E) Toomer’s personal views on race remain complex even in our own day.

SECTION 3
Time — 25 minutes
24 Questions
(25–39)

Directions: For each question in this section, select the best answer from among the
choices given and fill in the corresponding circle on the answer sheet.

Each sentence below has one or two blanks, each blank indicating that something has
been omitted. Beneath the sentence are five words or sets of words labeled A through
E. Choose the word or set of words that, when inserted in the sentence, best fits the
meaning of the sentence as a whole.
Example:

Hoping to ------- the dispute, negotiators proposed a compromise that they felt would
be ------- to both labor and management.
(A) enforce . . useful
(B) end . . divisive
(C) overcome . . unattractive
(D) extend . . satisfactory
(E) resolve . . acceptable

25. Unlike the other holiday travelers who argued impatiently, Francisco remained
-------, quietly waiting for his turn at the ticket counter.

(A) delighted (B) tranquil (C) confused (D) anxious (E) brusque
26. It is possible a cryptologist could have ------- the unique markings in the coded
message, but to us they were -------.
(A) unscrambled . . accessible
(B) obstructed . . concealed
(C) interpreted . . indecipherable
(D) deciphered . . straightforward
(E) deflected . . provided

27. In spite of the health department’s massive efforts to annihilate it, the deadly
virus pandemic -------.

(A) ebbed (B) eradicated (C) escalated (D) inflamed (E) abridged
28. The ------- of diverse Scottish clans is represented by the vast number of official
tartan cloths, where every different style and color of plaid represents a
unique clan -------.

(A) plethora . . transmission
(B) dearth . . separation
(C) devotion . . personality
(D) variety . . textile
(E) abundance . . identity
29. For Carlos, any dairy products he ate after his bout of food poisoning were
instantly nauseating; cheese and yogurt, therefore, were ------- to him.
(A) delectable (B) nutritious (C) abhorrent (D) expeditious
(E) assuaging

The passages below are followed by questions based on their content; questions

following a pair of related passages may also be based on the relationship between the

paired passages. Answer the questions on the basis of what is stated or implied in the
passage and in any introductory material that may be provided.
Questions 30-31 are based on the following passage.

30. The primary purpose of the passage is to
(A) imply that good health is similar to a good police force
(B) illustrate the different roles of the immune system
(C) emphasize the dangers of improper hygiene
(D) criticize criminals for their actions
(E) explain the ranking system for law enforcement

31. In the passage, the author makes use primarily of

31. In the passage, the author makes use primarily of
(A) hyperbole
(B) dramatic irony
(C) foreshadowing
(D) extended analogy
(E) satire

Questions 32-33 are based on the following passage.

32. The financial adviser suggests that the most important professional
relationships are

(A) built on a foundation of trust
(B) profitable for both the client and the adviser
(C) assessed thoroughly by both parties
(D) centered around hefty promises
(E) formed from the same model for each client
33. According to the passage, Kerrigan’s style of honesty even when it’s not
necessarily good news will benefit the advisers by

(A) earning them large payoffs from happy clients
(B) validating their work in the field
(C) creating solid connections with clients
(D) allowing them to promise clients great things
(E) increasing their word-of-mouth business

Questions 34-39 are based on the following passages.
The following passages were adapted from two novels published in 2012. The hockey
team the Montreal Canadiens is known in French by the nickname “les Habitants.”

34. In context, the phrase “bouncing and careening” (line 5) primarily serves to

34. In context, the phrase “bouncing and careening” (line 5) primarily serves to
demonstrate Antoine’s

(A) scorn for the poor acoustics in a hockey arena
(B) love of the excitement involved in tracking a hockey game
(C) sarcastic attitude toward hockey announcers in general
(D) basic disapproval of the new hockey announcer’s style
(E) inability to focus on the puck during hockey games
35. The author of Passage 2 would most likely view the observation in lines 10-11,
Passage 1 (“He … wanted”), as

(A) surprising, because hockey announcers and salesmen are so dissimilar
to one another

(B) distasteful, because it suggests that the two authors have different levels
of respect for hockey announcers

(C) bizarre, because salesmen are typically less prone to overstatement than
hockey announcers

(D) agreeable, because the two share similar attitudes toward how hockey
announcers should broadcast

(E) amusing, because hockey announcers do not generally major in business
in college

36. Passage 1 serves as evidence that the assertion in lines 30-34, Passage 2
(“Though … exciting”), is

(A) untrue in some cases
(B) folksy and hackneyed
(C) no longer applicable
(D) purposefully misleading
(E) unnecessarily pessimistic
37. The author of Passage 2 uses the word “dispassionate” (line 36) to describe

37. The author of Passage 2 uses the word “dispassionate” (line 36) to describe
action that is

(A) firm but unemotional
(B) unloving but persuasive
(C) disdaining but accurate
(D) calm but unsure
(E) educating but dull
38. The author of Passage 2 would consider Pierre (Passage 1) to be
(A) obviously motivated by business goals
(B) a good representative of a type of hockey announcer
(C) novel but unduly dismissed by listeners
(D) a type of announcer that should be removed from hockey
(E) unaware of the contemporary trends in broadcasting
39. In Passage 2, the author’s attitude toward Dan Schantz is best described as one
of

(A) unfettered disapproval
(B) complete lionization
(C) measured approval
(D) affected ambivalence
(E) sarcastic irritation

Questions 40-48 are based on the following passage.
The following excerpt is adapted from a 1985 book on the role of storytelling in human
understanding.

40. In line 1, “yarns” most nearly means

40. In line 1, “yarns” most nearly means
(A) strings
(B) tapestries
(C) writings
(D) narratives
(E) tails
41. The author implies that “nearby dots to be connected” (line 4) are details that
(A) are part of the simplicity of the meaning of life
(B) create exciting patterns and repetitions
(C) do not exist in the real world
(D) different personalities understand in different ways
(E) may not be connected outside the human mind
42. The author uses the phrase “twisted and mangled” (lines 7-8) in order to
(A) chastise readers for accepting simple solutions
(B) show the historical roots of a human response
(C) identify why humans prefer certain types of personality
(D) underline the need for a particular preference
(E) admire humans’ ability to understand difficult subjects

43. In context, the reference to “the ongoing plot” (line 14) serves to emphasize

43. In context, the reference to “the ongoing plot” (line 14) serves to emphasize
the

(A) historical interest in conspiracy theories
(B) challenge in uncovering historical mysteries
(C) perceived relatedness of historical events
(D) human talent for creating fictional stories
(E) smaller stories within large historical events
44. The phrase “In the grander scheme” (lines 17-18) serves as a transition
between a discussion of

(A) historical events and literary texts
(B) a contested theory and scientific certainty
(C) a neuroscientist’s view and a psychologist’s critique
(D) a general theory and a specific application
(E) a confessional memoir and a historical narrative
45. Based on information presented in lines 38-55, which of the following would
most likely be the title of a study of human personality in the twentieth
century?

(A) The Tragic Flaw in Human Personality
(B) Who We Are In Three Easy Steps
(C) The Mirror and the Labyrinth of Personality
(D) The Role of the American Civil War in History
(E) You Are a Good Person!

46. The author refers to a “cultural shift” (line 44) to help account for

46. The author refers to a “cultural shift” (line 44) to help account for
(A) the historically consistent understandings of personality
(B) psychologists’ desires to do away with storytelling
(C) the primary supply of contemporary popular fictional stories
(D) a general human distrust of psychological theories
(E) the broad historical change in attitudes toward personality
47. In line 49, “contain” most nearly means
(A) hold
(B) understand
(C) imprison
(D) restrain
(E) comprise
48. Which of the following best captures the main idea in lines 54-55
(“Because … we?”)?

(A) Our historical era is just as important as other past eras.
(B) Most stories we tell ourselves have deep historical roots.
(C) People in the future will tell themselves different stories from the ones
we tell ourselves.

(D) History is ultimately very similar to writing fiction or poetry.
(E) Life as we know it would be much different without the need for
narrative.

SECTION 2
Time — 25 minutes
20 Questions
(1–20)
Directions: For this section, solve each problem and decide which is the best of the
choices given. Fill in the corresponding circle on the answer sheet. You may use any
available space for scratchwork.

Notes
1. The use of a calculator is permitted.
2. All numbers used are real numbers.
3. Figures that accompany problems in this test are intended to provide information
useful in solving the problems. They are drawn as accurately as possible

EXCEPT when it is stated in a specific problem that the figure is not drawn to
scale. All figures lie in a plane unless other wise indicated.

4. Unless otherwise specified, the domain of any function f is assumed to be the set
of all real numbers x for which f(x) is a real number.

Reference Information

The number of degrees of arc in a circle is 360.
The sum of the measures in degrees of the angles of a triangle is 180.

1. If y is divisible by 2, 4, and 5, what is the least possible integer value of y ?

1. If y is divisible by 2, 4, and 5, what is the least possible integer value of y ?
(A)

8

(B) 10
(C) 20
(D) 40
(E) 50

2. What is the value of z in the figure above?
(A) 50
(B) 45
(C) 40
(D) 35
(E) 30

3. Of 45 books on a shelf,

are biographies. If 3 of the biographies are not about

women, how many of the biographies are about women?
(A) Five
(B) Six
(C) Seven
(D) Eight
(E) Nine

4. For some positive integer t, if t2 = 16, what is the value of (t – 1)2?
(A) –5
(B) –3
(C)

3

(D)

4

(E)

9

5. If the sum of a and 3a is less than the sum of 5b and –b, which of the following
must be true?

(A) a < 0
(B) b < 0
(C) a < b
(D) a = –b
(E) b = 0

A = {1, t, 7}

A = {1, t, 7}
B = {2, t, 6}

6. If the average (arithmetic mean) of set A is 4, what is the average of set B ?
(A) 4
(B) 4
(C) 5
(D) 5
(E) 6

=9
7. If the equation above is satisfied by the positive number p, what is the value of
p, rounded to the nearest integer?
(A) 4
(B) 5
(C) 6
(D) 7
(E) 8

8. In the xy-plane, the coordinates of point F are (–1, –3) and the coordinates of

8. In the xy-plane, the coordinates of point F are (–1, –3) and the coordinates of
point G are (–1, 0). If G is the midpoint of
point H ?

(A) (1, –3)
(B) (0, –3)
(C) (–1, 3)
(D) (–1, 6)
(E) (–3, 0)

, what are the coordinates of

9. According to the table above, if a woman’s ring diameter is 16 millimeters
what is her ring size?
(A) 5
(B) 5
(C) 6
(D) 6
(E) 7

10. If the equation y =

is true for all positive integer values of x, what could

be the value of y ?
(A)
(B)
(C)
(D)
(E)

11. If p < 6 and q < 12, which of the following must be true?
I. p + q < 18
II. q – p > 6
III. 2p = q
(A) I only
(B) II only
(C) III only
(D) I and II
(E) I and III

12. In the figure above, a || b, c || d, and r = 140. What is the value of s ?
(A) 30
(B) 40
(C) 45
(D) 50
(E) 60

13. Each of the blocks in a toy bin is either red, blue, or yellow. The number of
yellow blocks is 3 more than the number of red blocks, and the number of

blue blocks is 2 times the number of yellow blocks. Which of the following
could be the total number of blocks in the toy bin?
(A)

7

(B) 10
(C) 14
(D) 15
(E) 17

14. If the above functions are defined for all values of x, what is the value of k(4) ?
(A)

2

(B)

4

(C)

8

(D) 20
(E) 27

15. The chart above shows the types of businesses in a certain town as a percent of
the total number of businesses in the town. If there are 100 clothing stores,
how many more book stores are there than jewelry stores?
(A)

10

(B)

15

(C)

25

(D)

35

(E) 105

16. Triangle ABC lies in the xy-plane such that vertex A is at (m, 2n) and vertex B

16. Triangle ABC lies in the xy-plane such that vertex A is at (m, 2n) and vertex B
is at (2m, 4n), where m and n are both positive. Which of the following is the
equation of the line containing side
(A) y =

x

(B) y =

x

(C) y =

x+m

(D) y =

x

(E) y =

x+n

?

17. Amy’s closet contains shoes of different styles and colors. If all the boots in

Amy’s closet are black, which of the following statements about the shoes in
the closet must be true?

I. If a shoe is not a boot, then it is not black.
II. If a shoe is black, it is a boot.
III. If a shoe is not black, it is not a boot.
(A) I only
(B) II only
(C) III only
(D) I and II
(E) II and III

18. In the figure above, three tennis balls fit exactly inside a tube, just touching

the top, bottom, and sides of the tube. If the diameter of each tennis ball is d,
what is the volume of the tube in terms of d ?
(A) πd2
(B) 2πd2
(C)

d3

(D) πd3
(E) 3πd3

19. How many positive four-digit integers have a 7 in the hundreds place, a 1 in

the tens place, a prime number in the ones place, and exactly one of the digits
equal to 2 ?
(A) 10
(B) 11
(C) 12
(D) 13
(E) 14

20. Side

in isosceles triangle TUV is shorter than the other two sides. If the

20. Side

in isosceles triangle TUV is shorter than the other two sides. If the

degree measure of ∠V is divisible by 10, what is the smallest possible measure
of ∠T ?

(A) 40
(B) 45
(C) 50
(D) 60
(E) 65

SECTION 4
Time — 25 minutes
18 Questions
(21–38)
Directions: For this section, solve each problem and decide which is the best of the
choices given. Fill in the corresponding circle on the answer sheet. You may use any
available space for scratchwork.

Notes
1. The use of a calculator is permitted.
2. All numbers used are real numbers.
3. Figures that accompany problems in this test are intended to provide information
useful in solving the problems. They are drawn as accurately as possible

EXCEPT when it is stated in a specific problem that the figure is not drawn to
scale. All figures lie in a plane unless other wise indicated.

4. Unless otherwise specified, the domain of any function f is assumed to be the set
of all real numbers x for which f(x) is a real number.

Reference Information

The number of degrees of arc in a circle is 360.
The sum of the measures in degrees of the angles of a triangle is 180.

21. If p + 3 = 12 and p – q = 5, what is the value of q ?

21. If p + 3 = 12 and p – q = 5, what is the value of q ?
(A)

4

(B)

6

(C)

9

(D) 10
(E) 20

A is the set of even integers.

B is the set of multiples of 9.

C is the set of the factors of 60.
22. Which of the following is a member of both sets A and B, but not of set C ?
(A)

6

(B)

9

(C) 12
(D) 15
(E) 18

23. In the scatter plot above, Tisha’s time for each of 12 workouts is plotted

against the number of calories burned during that workout. During how many
workouts did Tisha exercise for more than 25 minutes and burn more than
400 calories?

(A) Two
(B) Three
(C) Four
(D) Five
(E) Six

24. In the xy-coordinate plane above, line m passes though points (–3, 5) and (8,

5) as shown. Line p (not shown) is perpendicular to line m and passes through
point (3, 8). Which point lies on both line m and line p ?
(A) (8, 3)
(B) (6, 5)
(C) (5, 8)
(D) (3, 8)
(E) (3, 5)

25. In the figure above, O is the center of the circle and points R and S lie on the

circle. If ∆RST is equilateral with a perimeter of 54, what is the circumference
of the circle?
(A) 81π
(B) 54π
(C) 36π
(D) 27π
(E) 18π

26. On the number line above, the tick marks are equally spaced. If y + z = 2,
what is the value of x ?
(A) –1
(B) –1
(C) –1
(D) –1
(E) –1

27. A certain recording studio produced 1 hit record in its first year of business.

After the first year, the total number of hit records produced doubled every 6
months. Which of the following expresses the total number of hit records

produced by the studio in t years after the first year of business? (Assume that
t is a positive integer.)
(A) 22t
(B) t6
(C) 2t
(D)
(E)

28. In the graph above, the parabola is symmetrical across the line x = −1 . If
the x-intercepts of the parabola are (–5, 0) and (m, 0), what is the value of m ?
(A)
(B) 1
(C) 1
(D) 2
(E) 3

x, y, 36, 108, …
29. The first term of the sequence above is x. If each term after the first is three
times the previous term, what is the value of x ?

30. The price P, in dollars, of a certain stock m months after it was bought is given
by the equation P(m) = 125,000

. What is the price, in dollars, of the

stock 15 months after it was bought? (Disregard the $ sign when gridding in
your answer.)

31. In the figure above, if ACBD is a square and line m passes through point C,
what is the value of y ?

32. A bag of 40 marbles contains only marbles that are either red or blue. If the

probability of choosing a red marble is 5 out of 8, how many blue marbles are
in the bag?

33. The base of triangle A is three times that of triangle B and the height of

triangle A is two times that of triangle B. If triangle A has an area of 120,
what is the area of triangle B ?

34. Sue and David together own 57 hamsters. If David owns 5 more than 3 times
the number of hamsters that Sue owns, how many hamsters does Sue own?

35. In the figure above,

bisects ∠COG,

bisects ∠AOE,

bisects ∠AOC, and

bisects ∠EOG. The measure of ∠COG is what fraction of the measure of

∠AOF ?

36. If the reciprocal of a number is greater than the square of that number, what is
one possible value for the number?

37. The appendix of a certain book starts on this page and contains 7 sections. The
sections are consecutive, and each section is exactly five full pages. No section
shares a page with any other section. On what page is the last page of the
appendix?

38. If

=

and

= , what is the value of

?

SECTION 5
Time — 30 minutes
39 Questions
(1–39)
Directions: For each question in this section, select the best answer from among the
choices given and fill in the corresponding circle on the answer sheet.

The following sentences test correctness and effectiveness of expression. Part of each

sentence or the entire sentence is underlined; beneath each sentence are five ways of
phrasing the underlined material. Choice A repeats the original phrasing; the other

four choices are different. If you think the original phrasing produces a better sentence
than any of the alternatives, select choice A; if not, select one of the other choices.

In making your selection, follow the requirements of standard written English; that is,

pay attention to grammar, choice of words, sentence construction, and punctuation.
Your selection should result in the most effective sentence—clear and precise, without
awkwardness or ambiguity.
EXAMPLE:
Bobby Flay baked his first cake and he was thirteen years old then.
(A) and he was thirteen years old then
(B) when he was thirteen
(C) at age thirteen years old
(D) upon the reaching of thirteen years
(E) at the time when he was thirteen

1. An opener for 1999’s Geniuses, Savants, and Prodigies conference, the piano was

1. An opener for 1999’s Geniuses, Savants, and Prodigies conference, the piano was
first played by David Helfgott when he was five years old.

(A) the piano was first played by David Helfgott when he was five years old
(B) the first playing of the piano by David Helfgott was when he was five
years old

(C) David Helfgott began playing the piano when he was five years old
(D) David Helfgott, who began playing the piano at five years old
(E) David Helfgott, who first played the piano when he was five years old
2. The dodo bird, a flightless bird once native to the island of Mauritius, that was
being discovered in 1598.

(A) that was being discovered
(B) with its discovery
(C) discovered
(D) having been discovered
(E) was discovered
3. The stock market crashed heavily in 1929, the initiating thereby of an
economic depression that devastated the nation.
(A) the initiating thereby of
(B) thereby initiating
(C) it initiated thereby
(D) which thereby made it initiate
(E) thereby it initiated

4. Determined to finish the game despite the rain, the football team’s fight for the

4. Determined to finish the game despite the rain, the football team’s fight for the
trophy was impressive.

(A) the football team’s fight for the trophy was impressive
(B) the football team fought impressively for the trophy
(C) the trophy for which the football team impressively fought
(D) the trophy was what the football team impressively fought for
(E) the football team’s impressive fight was for the trophy
5. Being only a thousandth of a millimeter wide, even when produced by the

largest spiders, are cobwebs, delicate strands that are five times stronger than
steel strands of the same thickness.

(A) Being only a thousandth of a millimeter wide, even when produced by
the largest spiders, are cobwebs,

(B) Even when produced by the largest spiders, cobwebs, they are only a
thousandth of a millimeter wide,

(C) Cobwebs, while being barely a thousandth of a millimeter wide, even
when produced by the largest spiders,

(D) Only a thousandth of a millimeter wide, even when produced by the
largest spiders, cobwebs are

(E) Though only a thousandth of a millimeter wide, even when produced by
the largest spiders, cobwebs as

6. The Coronation of Napoleon, by Jacques-Luis David, an awe-inspiring and
enormous painting that covers nearly 650 square feet.

(A) an awe-inspiring and enormous painting that covers
(B) is an awe-inspiring and enormous painting that covers
(C) which is an awe-inspiring and enormous painting covering
(D) who created an awe-inspiring and enormous painting that covers
(E) awe-inspiring as an enormous painting that covers

7. The new phone cost almost nothing after deducting the rebate from its original
price.

(A) after deducting the rebate
(B) following the deducting of the rebate
(C) of the deducting of the rebate
(D) since the deducting of the rebate
(E) after the rebate was deducted
8. Tsar Nicholas II’s violent dictatorship resulted in them eventually revolting
against his brutality.

(A) Tsar Nicholas II’s violent dictatorship resulted in them eventually
revolting against his brutality.

(B) Violent dictatorship, practiced by Tsar Nicholas II, eventually resulted
in their revolting against his brutality.

(C) Tsar Nicholas II’s violent dictatorship led to an eventual revolt against
his brutality.

(D) Tsar Nicholas II dictated violently, which is why many eventually
revolted against his brutality.

(E) They revolted against his brutality and it was because of the violent
dictatorship of Tsar Nicholas II.

9. Lindsay was needing to buy a new car, she went to the local car dealership to

9. Lindsay was needing to buy a new car, she went to the local car dealership to
do that.

(A) Lindsay was needing to buy a new car, she went to the local car
dealership to do that.

(B) Needing to buy a new car, Lindsay went to the local car dealership.
(C) Having gone to the car dealership, buying a new car was what Lindsay
needed.

(D) Going to the car dealership was Lindsay, where she needed to buy a
new car.

(E) Lindsay went to the car dealership, she needed to buy a new car.
10. The detectives identifying the criminal, they were determined to catch the
man who stole the jewelry.

(A) The detectives identifying the criminal, they
(B) To identify the criminal, the detectives
(C) The detectives identified the criminal, they
(D) Identifying the criminal, was why the detectives
(E) Having identified the criminal, the detectives
11. Wanting more responsibility and to increase their monthly earnings, many
employees volunteer to work overtime.

(A) Wanting more responsibility and to increase their monthly earnings,
(B) More responsibility and an increase in their monthly earnings are
wanted by

(C) To want more responsibility and increase their monthly earnings is why
(D) While wanting more responsibility and an increase in their monthly
earnings, then

(E) Wanting more responsibility and an increase their monthly earnings,
12. The diverse works of Igor Stravinsky ranges from Russian ballets to

12. The diverse works of Igor Stravinsky ranges from Russian ballets to
neoclassical compositions and chamber works.
(A) ranges
(B) having ranged
(C) range
(D) that range
(E) ranging
13. Many authors of the 1920s wrote novels that included so much symbolism that
the works are often difficult to comprehend; such symbolism obscures, rather
than clarifies, the author’s main point.

(A) that the works are often difficult to comprehend; such symbolism
(B) that the works, being often difficult to comprehend and symbolizing
(C) and the works are often difficult to comprehend, and they symbolize
(D) being often difficult to comprehend, such work symbolizes and
(E) that their works are often difficult to comprehend and symbolizing
14. In 1917 the Anti-Saloon League urged that the sale, production, and

transportation of alcohol being banned in the United States, thus initiating the
movement that led to the Prohibition.

(A) being banned in the United States, thus initiating
(B) should be banned in the United States for initiating
(C) have a ban in the United States, which initiated
(D) be banned in the United States, thus initiating
(E) ought to be banned in the United States for initiating

15. Charlemagne was crowned in 768 A.D. as King of the Franks, he was the oldest

15. Charlemagne was crowned in 768 A.D. as King of the Franks, he was the oldest
son of Pepin the Short and Bertrada of Laon.
(A) Charlemagne was crowned in 768 A.D. as King of the Franks, he was
(B) In 768 A.D. they crowned Charlemagne as King of the Franks, having
been
(C) Charlemagne, in 768 A.D. crowned as King of the Franks, and he was
(D) Crowned in 768 A.D. as King of the Franks, Charlemagne was
(E) Charlemagne, in 768 A.D. he was crowned as King of the Franks, was
16. Light bulbs generate their light when a filament in its center is heated to a
high temperature until the filament glows.
(A) Light bulbs generate their light
(B) A light bulb generates light
(C) A light bulb’s light, generated
(D) The light bulb generates their light
(E) The light of light bulbs are generated
17. Local restaurant critics consider the baked haddock at the new seafood

restaurant on Main Street as being able to be considered among the worst they
have ever tasted.

(A) as being able as to be considered
(B) that it is
(C) to be able to be considered
(D) to be
(E) as to be

18. Ernest Hemingway, who began his career as a journalist for The Kansas City

18. Ernest Hemingway, who began his career as a journalist for The Kansas City

Star, and created a concise writing style that was different from that of any
other American writer of his day.

(A) and created a concise writing style that was different from that of any
other American writer

(B) would create a writing style that was different from any other American
writer

(C) and would create a writing style that was different from any other
American writer

(D) created a concise writing style that was different from that of any other
American writer

(E) created a concise writing style that was differing with the style created
by any other American writer

19. The crusaders of the Middle Ages, according to historians, succeeded not in

gaining access to Jerusalem, but only to leave a trail of devastation in their

wake as they devastated Mediterranean ports and fought among themselves.
(A) The crusaders of the Middle Ages, according to historians, succeeded
not in gaining access to Jerusalem, but only to leave

(B) The crusaders of the Middle Ages, according to historians, succeeded
not to gain access to Jerusalem, but only in leaving

(C) The crusaders of the Middle Ages, according to historians, succeeded
not in gaining access to Jerusalem, but only in leaving

(D) According to historians the crusaders of the Middle Ages succeeded not
in gaining access to Jerusalem but only to leave

(E) According to historians the crusaders of the Middle Ages, they did not
succeed in gaining access to Jerusalem but instead they left

20. The reputations of either of the shows appears to be well-merited.

20. The reputations of either of the shows appears to be well-merited.
(A) The reputations of either of the shows appears to be well-merited.
(B) Either of the shows appears to have merited their reputation.
(C) Either of the shows appear to have merited the reputation.
(D) Either of the shows appears to have merited its reputation.
(E) The reputation of either of the shows appears to be well-merited.

The following sentences test your ability to recognize grammar and usage errors. Each

sentence contains either a single error or no error at all. No sentence contains more
than one error. The error, if there is one, is underlined and lettered. If the sentence
contains an error, select the one underlined part that must be changed to make the

sentence correct. If the sentence is correct, select choice E. In choosing answers, follow
the requirements of standard written English.
EXAMPLE:

21.

22.

23.

24.

24.

25.

26.

27.

28.

28.

29.

30.

31.

31.

32.

33.

34.

Directions: The following passage is an early draft of an essay. Some parts of the
passage need to be rewritten.

Read the passage and select the best answers for the questions that follow. Some

questions are about particular sentences or parts of sentences and ask you to improve
sentence structure or word choice. Other questions ask you to consider organization

and development. In choosing answers, follow the requirements of standard written
English.

Questions 35-39 are based on the following passage.
(1) People are rarely grateful for the things that they have until after they lose

them. (2) After that what takes places is compelling them realize the value of their

friends, family, and possessions, and hopefully, to gain greater appreciation for the
truly important things in life.

(3) One novel illustrates this point in an especially effective manner. (4) The

Prince and the Pauper is a work of fiction written in 1881 by Mark Twain. (5) This
book demonstrates the lesson through the story of Tom Canty, a poor boy from
London. (6) In this book, Tom changes places with Prince Edward, whom he

resembles very closely. (7) At first, Tom imagines that life as a wealthy prince will
be perfect, but he soon discovers that the court customs and rules are more

complicated than he had thought, and he longs to return to his family and even to
the poverty of his former life. (8) When he finally does return home, he is

appreciative of the few things that he does have and no longer envies those who
only appear to have happiness.

(9) When we lose someone dear to us, or an important object, and then grow in

appreciation for that person or thing, we are learning the same lesson that Tom

learned. (10) It is possible to recognize the value of those who love us before we
lose them. (11) Many people believe that Prince Edward is a more engaging

character than Tom. (12) However, this is a lesson that some learn only after it is

too late. (13) Instead, they spend their whole lives longing for their own “prince”
with whom they can trade places. (14) They fail to acknowledge just how

fortunate they already are. (15) Like Tom before he met Prince Edward, they

imagine that wealth is the key to happiness, and overlook the fact that many of the
happiest people who have lived have been those who possessed relatively little.

35. In context, which of the following is the best version of the underlined section
of sentence 2 (reproduced below)?

After that what takes places is often compelling them to realize the value of their

friends, family, and possessions, and hopefully, to gain greater appreciation for the
truly important things in life.
(A) (As it is now)
(B) After that, however, they are often compelled
(C) Such a tragedy then occurs that often compels them
(D) You are often compelled
(E) Then what occurs is the person will often be compelled

36. In context, which of the following is the best way to combine sentences 4 and

36. In context, which of the following is the best way to combine sentences 4 and
5 (reproduced below)?

The Prince and the Pauper is a work of fiction written in 1881 by Mark Twain.

This book demonstrates the lesson through the story of Tom Canty, a poor boy from
London.

(A) The Prince and the Pauper is a work of fiction written in 1881 by Mark

Twain, and it demonstrates the lesson through the story of Tom Canty,
a poor boy from London.

(B) The Prince and the Pauper, a work of fiction written by Mark Twain in

1881, demonstrates this lesson through the story of Tom Canty, a poor
boy from London.

(C) The story of the poor London boy Tom Canty, which demonstrates the
lesson; The Prince and the Pauper is a work of fiction written by Mark
Twain in 1881.

(D) The story of Tom Canty is a work of fiction written in 1881 by Mark

Twain, a poor boy from London, The Prince and the Pauper demonstrates
the lesson.

(E) The Prince and the Pauper is a work of fiction written by Mark Twain in
1881, demonstrating the lesson through the story of poor London boy
Tom Canty.

37. Which of the following, if added after the second paragraph, would most

37. Which of the following, if added after the second paragraph, would most
improve the essay?

(A) A paragraph detailing what Tom missed from his home in London and
why those things were more important to him than the wealth he
enjoyed in Prince Edward’s court.

(B) A paragraph explaining why the court customs in Prince Edward’s court
were more intricate than those of surrounding courts.

(C) A paragraph discussing the reason that Tom’s family became povertystricken.

(D) A paragraph outlining the literary devices that Mark Twain used to

demonstrate how Tom gained an appreciation for his home in London.

(E) A paragraph showing how Mark Twain learned to appreciate his family
and friends before he lost them in death.

38. In context, which of the following is the best combination of sentences 13 and

38. In context, which of the following is the best combination of sentences 13 and
14 (reproduced below)?

Instead, they spend their whole lives longing for their own “prince” with whom they
can trade places. They fail to acknowledge just how fortunate they already are.

(A) Instead spending their lives longing for their own “prince” with whom
they can trade places, one fails to acknowledge just how fortunate one
already is.

(B) After you stop longing for your own “prince” with whom you can trade
places, you will acknowledge how fortunate you are.

(C) Before you can acknowledge just how fortunate you are, you must

instead stop longing for your own “prince” with whom you can trade
places.

(D) Instead, they spend their whole lives longing for their own “prince”

with whom they can trade places and they have failed to acknowledge
just how fortunate they already are.

(E) Instead, they spend their whole lives longing for their own “prince”

with whom they can trade places, and fail to acknowledge just how
fortunate they already are.

39. Deleting which of the following sentences would improve the essay?
(A) Sentence 3
(B) Sentence 4
(C) Sentence 8
(D) Sentence 9
(E) Sentence 11

DRILLS ANSWERS

You will find a detailed explanation for each question beginning on
this page.

Chapter 6
Drills: Answers and Explanations

Section 1
1. B The sentence tells you the semester had been challenging and
stressful, which would be a negative thing. Since is a change
direction trigger, so you know the missing word will have
something to do with the students getting a break from the
school. Choice (B) makes the most sense.
2. E Start with the second blank. Because Henry got a position as
a starter on the varsity team, you know he’s a good athlete. If
his teammates are second-string and jealous of his success, we
know they aren’t as good as Henry. You can easily eliminate
choice (B). Now that you know the teammates are jealous,
go back to the first blank. The missing word must have
something to do with them being jealous. Envy means a
feeling of discontent with another’s advantage, so choice (E) is
the best answer.
3. E The sentence tells you that Einstein is one of the most famous
scientists in the world, so his winning the Nobel Prize would
only increase that fame. The first blank must mean
something like increase or earn, so you can eliminate choices
(B), (C), and (D). Continuing with those same clues, the
second blank must mean something like fame or attention.
Between choices (A) and (E), choice (E) is the best answer.
4. C The sentence gives you examples of the black mamba snake’s
lethality, so the missing word must mean something about
being poisonous. Virulent means venomous hostility, so
choice (C) is the best answer.
5. E Because the reviewer denounced the acting, you know the
missing word will be negative. The colon is a same
direction trigger, so what follows gives you more

information about the missing word. The actress’s style is
flat and tedious. Since monotonous means lacking in variety or
tediously unwavering, choice (E) is definitely the best answer.
6. A The definition of the missing word is included in this
sentence: speaking at inordinate length to obstruct a legislative
assembly. Choice (A), filibustering, is the word that matches
that definition, so it is the correct answer.
7. A Do the first blank first. A wide-reaching enterprise with a
monopoly on a market is likely to drive up prices and take
advantage of consumers. You can eliminate choices (D) and
(E). In order to avoid the monopoly, it’s necessary to have
other businesses, or competition, in the market. Therefore,
choice (A) is the best answer.
8. C Do the second blank first. Because the first part of the
sentence tells you that a vast majority … are advantageous,
the blank that refers to the preponderance must also mean
advantageous. Choices (B) and (D) can easily be eliminated.
Then go back to the first blank. If you are trying to
distinguish pathogens from bacteria that are advantageous,
the first blank must be a negative word. The pathogens are
not helping the host (allies), nor are they indicating the future
(portent), so you can also eliminate choices (A) and (E).
Choice (C) is the right answer.
9. E Both Locke and Hebb agree that environmental factors are
important to human development. However, Locke believes
that the environmental factors are the only influence, so you
can eliminate choices (B) and (D). Hebb never mentions
anything about tabula rasa, so you can eliminate choice (A).
Neither mentions government regulations at all, so that one
can also be eliminate, leaving you with choice (E), the right
answer.

10. D Hebb uses the analogy to explain how the two ideas are so
tightly knitted, it’s impossible to say which determines an
individual’s characteristics. Be careful about choice (C). It
looks good at first, but the question is asking about nature
specifically, not the general meaning of the analogy. Choice
(D) is the right answer.
11. C Locke felt that experience was the only way humans learn
and develop. He said that we are born blank slates and that
our experiences must “write” who we are on our minds. There
are no innate characteristics. Choice (C) is the best answer.
12. C Passage 1 is a theory from a seventeenth-century philosopher
and Passage 2 is the viewpoint of a twentieth-century
psychologist. Eliminate choice (B), because the Passage 1 is
not the modern assumption. Choice (D) is also wrong,
because only one perspective is presented in Passage 1.
There is no problem/solution, so also eliminate choice (E).
Choice (C) is the right answer.
13. A Although the first few paragraphs detail Toomer’s
importance during the Harlem Renaissance, the end of the
passage states that Toomer’s early literary output can be more
thoroughly understood than his later personal life. Choices (B)
and (C) are disproven in the first paragraph, and choice (E)
is disproven in the fourth paragraph. Choice (D) is also
slightly off: it cannot be said that Toomer’s essays were
inconsistent, only that there were so few of them.
14. C Because these two paragraphs are particularly about Jean
Toomer, choices (A) and (E) can be eliminated. Both
paragraphs are concerned with how other artists and
thinkers thought of Toomer, however, so the best answer
must be (C).
15. E Because Braithwaite’s review of Cane is so glowing, his

praise can be described as total or complete, as in choice (E).
All other choices provide alternate meanings of the word
“unreserved,” but they do not work in this context.
16. E The first paragraph states, Toomer gained huge accolades from
the white literary world as well, and well-known authors such
as Sherwood Anderson and Waldo Frank considered him one of
their own. In this context, Sherwood Anderson and Waldo
Frank are used as representatives of the white literary world,
lending support to choice (E). Choice (A) cannot work
because there is no indication that Toomer was courting
this white readership, particularly not with any urgency.
17. D The sentence in question is the topic sentence of the second
paragraph. It introduces the ideas that are to come. The
paragraph goes on to say that Toomer could incorporate
influences from white as well as black artists, and he melded
them into a new, innovative style that mixed poetry, prose, jazz,
folklore, and spiritualism. As in choice (D), these are aspects
of Toomer’s art that showed black and white artists alike a
new artistic freedom.
18. A The sentence that directly precedes “These scraps” is as
follows: Toomer himself may not have thought of these
marriages as interracial: particularly by the 1940s, Toomer
insisted that his race was “American” and by the end of his life,
he may have even identified as a white man. The repetition of
the word may shows the author’s uncertainty as to Toomer’s
exact attitudes. “These scraps” must then refer to the scant
biographical evidence that literary historians have in
piecing together Toomer’s later life, as suggested by choice
(A).
19. A The fourth paragraph discusses the increase in race activism,
though it says of Toomer, By then, and until his death in
1967, Toomer was much more taken with local issues, and his

main concern was with his church, the Friend’s Society of
Quakers, and the high school students whom he taught there. In
other words, Toomer was not as interested in race activism
as were many of his African American contemporaries. In
this sense, his views were atypical, as suggested by choice
(A). Choice (E) offers a similar answer, but it is too extreme
and is disproven by the quotation in the following
paragraph. It was not that he had no interest in
contemporary race relations but more that his interest was
different.
20. C Pay careful attention to the sentence that contains the word
in question: By then, and until his death in 1967, Toomer was
much more taken with local issues, and his main concern was
with his church, the Friend’s Society of Quakers, and the high
school students whom he taught there. “Taken with” in this
context means “occupied with” or “interested in,” and as
the sentence then states, Toomer was much more interested
in smaller, local problems than in national race problems.
21. B The topic sentence of this paragraph reads as follows: If
Toomer’s early literary output can be more thoroughly
understood than his later personal life, or his later racial
identification, it can only be because Toomer himself wanted it
to be so. This sentence suggests that the paragraph itself will
discuss Toomer’s own attitudes, eliminating choices (A) and
(D). We learn in earlier paragraphs that Toomer did not
have a typical “commitment to racial equality,” eliminating
choice (E), and he did not contradict himself in public and
private, eliminating choice (C). Only choice (B) reflects the
actual content of the paragraph.
22. E As the quotation from Toomer demonstrates, he saw race as
a more complex thing than mere black and white. We can
deduce, then, that he would’ve found the contemporary
debates far too simple, as choice (E) suggests. His own

views were “racially complex,” but “black and white” refers
to the contemporary debates in which Toomer was not a
participant, eliminating choice (C). We may consider his
views “socially progressive,” but the passage does not state
that they are, so choice (B) must also be eliminated.
23. B The sentence before the one cited in the question reads as
follows: Because Toomer was such a truly great artist, literary
historians will always long for more information about his life.
In other words, literary historians would like more information
about his life. Among the answer choices, choice (B) would
best supply this information.
24. E The full sentence in question reads as follows: We should be
wary of the rigid categories that Toomer fought against all his
life, and if anything, perhaps Toomer’s refusal to fit into these
categories can help us to modify our own. This sentence is a
reference to our own contemporary views on race, which,
the sentence suggests, Toomer might be able to help us
modify, as paraphrased in choice (E). Although we may
consider his views more advanced, the passage does not refer
to them in this way, eliminating choice (D).

Section 3
25. B The sentence tells you that the holiday travelers are arguing
impatiently. You have the change direction trigger of unlike,
so you know the missing word must mean the opposite of
that. Additionally, you know that Francisco was quietly
waiting. Tranquil means peaceful, calm, or quiet, so choice (B)
is the best answer.
26. C Do the first blank first. If there are unique markings in a
coded message, a cryptologist would be able to solve or
decode the message. Eliminate choices (B) and (E). The but
is a change direction trigger, so if the cryptologist is able to
decode the message, then the missing word would mean not
able to decode. Eliminate choices (A) and (D), leaving choice
(C) as the best answer.
27. C The health department is unleashing massive efforts to
annihilate, which would make it seem like the department is
stopping the pandemic. However, the in spite of trigger lets
you know the word will actually be the opposite of that, so
choice (C) is the best answer.
28. E Do the first blank first. The diverse Scottish clans are
represented by a vast number of tartan cloths, so the missing
word must mean large number. Eliminate choices (B) and
(C). The second blank refers to the connection between the
tartans and the clans themselves. It wouldn’t make sense
that the official tartans would represent a clan transmission,
so eliminate choice (A). Textile looks like a good option
since a tartan is a cloth, but the tartan is the cloth, not a
representation of the cloth, so you can also eliminate choice
(D). Choice (E) is the best answer.

29. C If the foods are instantly nauseating, they will be disgusting or
revolting. Choice (C) is the best answer.
30. B Although there is an analogy in the passage connecting the
immune system with the structure of law enforcement, that
analogy is used to explain the parts of the immune system.
The primary purpose of the passage is to describe that
system. Choice (A) can be eliminated because the passage
isn’t discussing good health—it’s simply discussing the parts
of the immune system. For that same reason, choice (C) can
also be eliminated. Choice (D) is irrelevant, loosely tied to
the law enforcement analogy, but just barely. Choice (E)
connects back to the analogy, but it’s not the primary
purpose of the passage. Choice (B) is the best answer.
31. D The passage compares the immune system to a law
enforcement structure, and then continues to make similar
connections on a more granular level. This is an extended
analogy, making choice (D) the best answer.
32. A The description of the style begins with always be honest and
then continues with even if statements. This lets you know
that the most important thing is the honesty. Although
profits, assessments, and promises are all mentioned in the
passage, it’s the honesty that is the most important quality.
Choice (A) is the best answer.
33. C At the end of the passage, Kerrigan says you will lose them
when they find you haven’t been honest. The honesty may or
may not result in large payoffs, validated work, or word-ofmouth business, but the passage clearly makes the
connection between honesty and solid client relationships.
Choice (C) is the best answer.
34. D Antoine of Passage 1 does not approve of the new
announcer, so his comparison of the announcer’s voice to a

hockey puck is unfavorable, eliminating choice (B). He is
commenting on one specific announcer, which eliminates
choice (C). Only choice (D) effectively captures Antoine’s
disapproving attitude.
35. D The line in Passage 1 offers Antoine’s critique of the new
announcer. Antoine’s preferred announcer, Pierre, is eventoned, almost dull. The author of Passage 2 likes similar
announcers, those whose announcing can be characterized
by dispassionate action. Therefore, the author of Passage 2
would likely find Antoine’s critique “agreeable,” as
suggested by choice (D). Choices (A), (B), and (E) should be
eliminated because they take the simile from Passage 1 too
literally.
36. A The author of Passage 1 describes two different announcers,
Pierre and Jack/Jimmy. Pierre is the type of announcer
described in the quoted lines from Passage 2. Jack/Jimmy,
however, is not characterized by this kind of even-tempered
commentary. Instead, the timbre of his voice flew around as
erratically as the puck itself, and Jack/Jimmy’s voice is
described as too-perfect. Although there is some indication
in Passage 1 that new announcers tend to be more
animated, there is no such indication in Passage 2, which
eliminates choice (C). Furthermore, although Antoine does
not like the new hockey announcer, his general attitude
cannot be described as “unnecessarily pessimistic,” because
it is not general enough to be so, which eliminates choice
(E).
37. A Passage 2 draws an analogy between good hockey
announcers and good parents and teachers. He stresses their
ability to educate in the face of anything or anyone, whether
punishingly dull or wildly exciting. He goes on to say, All of
them let you know that, rain or shine, at least someone is
keeping it together. The last sentence, particularly, indicates

someone who is firm and not overtaken by emotional
overstatements, as suggested in choice (A). Although part of
choice (E), “educating,” could work, there is no indication
that all “dispassionate action” is dull, only that it can be
when necessary.
38. B Antoine’s preferred announcer, Pierre, is even-toned, almost
dull. The author of Passage 2 likes similar announcers, those
whose announcing can be characterized by dispassionate
action. Therefore, Pierre could be a “good representative” of
a certain type of hockey announcer, as suggested by choice
(B). Although Pierre has been replaced, there is no
indication, particularly not in Passage 2, that such a type of
announcer would be “unaware” of the new type of
announcer, which eliminates choice (E).
39. C The author of Passage 2 has a positive attitude toward Dan
Schantz, so choices (A), (D), and (E) can be eliminated.
Choice (B), however, is too extreme an expression of a
positive attitude. Choice (C) is milder and more in keeping
with the tone of the essay, so it is the best choice.
40. D The phrase to spin yarns appears in the first sentence, and it
is reiterated in the later sentences in the paragraph, which
refer to some kind of narrative and our minds wanting stories.
While choices (A), (B), and (E) offer alternate meanings of
the word yarns, only choice (D) works in this context.
41. E The metaphor of connecting dots appears in this context: We
want any nearby dots to be connected. Effect with no cause,
correlation with no causation: we can’t assimilate these ideas
because they don’t have that narrative structure. In other
words, even if these dots aren’t connected, our minds want
them to be and thus connect them, as choice (E) suggests.
Although the connections may not exist in the real world,
the passage does not imply that the details themselves do

not exist, thus eliminating choice (C).
42. D The full sentence reads as follows: Our minds want stories,
even if those stories need to be twisted and mangled into
existence. In other words, we can have a difficult time
creating stories, but we have the need nonetheless, as
choice (D) suggests. The author does not reflect on whether
this is a good or bad trait, thus eliminating choices (A) and
(E). The discussion of history does not come until later in
the passage, thus eliminating choice (B).
43. C The phrase appears in this context: Historians and onlookers
alike have spent over a century debating the causes, the effects,
and the place of this event in the ongoing plot of American
history. Neuroscientists have referred to a “need for narrative.”
The passage as a whole is about narrative, and the word plot
relates to narratives, suggesting that the history of the
American Civil War is another one of these narratives, full
of related events, as choice (C) indicates. Choice (B) cannot
work because the plot referred to here is not that of a
mystery, nor are any historical mysteries discussed. The
author does not refer to this need for narrative as a special
talent, thus eliminating choice (D).
44. D The first two paragraphs discuss the need for narrative in a
general way, even citing the findings of neuroscientists and
the work of historians. The third and fourth paragraphs
focus more specifically on personality, which can be
explained with a specific application of the general theory
of the need for narrative. Choice (D) best captures this
transition. The latter half does discuss literary texts, but not
exclusively, and the first half is focused on much more than
historical events, so choice (A) can be eliminated. Choice (C)
cannot work because the “need for narrative” is ultimately a
psychological concept that is discussed throughout the
passage, and it is not critiqued.

45. C The early twentieth century is discussed in these lines: In the
early twentieth century, the very notion of “consistent” stories
broke down, and characters became less rigidly defined as a
result. Suddenly, amid a cultural shift away from religious
certainty, one’s environment, one’s historical era, one’s family
history could all come to bear on the maze of human
personality. In other words, this era was characterized by
complexity rather than simplicity, so any discussion of
personality must be more complex than the titles in choices
(A), (B), and (E). Choice (D) is off-topic. Only choice (C)
adequately captures the complexity described in the
passage.
46. E This shift away from religious certainty is discussed in these
lines: In the early twentieth century, the very notion of
“consistent” stories broke down, and characters became less
rigidly defined as a result. Suddenly, amid a cultural shift away
from religious certainty, one’s environment, one’s historical era,
one’s family history could all come to bear on the maze of
human personality. In other words, personality had become a
newly complex object with many things influencing it, as
choice (E) suggests. Choice (A) cannot work because
understandings of personality have not been consistent
throughout history. Choice (D) does not work because there
is no evidence in the passage that non-psychologists critique
the theories of psychologists.
47. B The word contain appears in this sentence: Psychologists
began to spend entire careers studying human personalities, but
for all these changes, the goal was still the same: contain the
human experience, find the story that can encapsulate all of
human complexity. Use the second part of the sentence as a
clue. The word contain must mean something like find the
story that can encapsulate, and the closest approximation
from this list of answer choices is choice (B). The other

choices offer synonyms for the word contain, but they do
not work in this particular context.
48. E The last sentence of a passage will typically offer some kind
of summary of a passage, and this sentence does just that.
The passage as a whole discusses the need for narrative in
many aspects of life, including how we understand
ourselves. The last sentence asks, rhetorically, Because after
all that has come before us, and all that will come later, if we’re
not part of the big story, what are we? Choice (E) captures
this basic idea well in suggesting that without the big story,
our lives would be different. Although the last sentence
does look to the future a bit, it does not make any claims
about the stories that people in the future will tell
themselves, thus eliminating choice (C). Also, while there
are some implied comparisons between the “narrative” of
history and that of fiction, these comparisons are not
addressed in this final sentence, eliminating choice (D).

Section 2
1. C When asked for the value of a variable, Plug In the Answers
(PITA). Starting with the least value, see if each answer is
divisible by 2, 4, and 5. 8 is divisible by 2 and 4 but not by
5, so (A) can be eliminated. 10 is divisible by 2 and 5 but
not by 4, so (B) can be eliminated. 20 is divisible by 2, 4
and 5, and it is the least number left on the list. Although
40 is also divisible by 2, 4, and 5, it is greater than 20, so
(D) can be eliminated. Choice (C) is the credited response.
2. A The angle in the upper right of the triangle is opposite the
45° angle, so it is also 45°. A triangle has 180°, so 85 + 45
+ z = 180. Therefore, 130 + z = 180, so z = 50. Choice
(A) is the credited response.
3. B There are 45 books on the shelf, of which

are biographies.

(45) = 9 biographies. 3 are not about women, and 9 – 3
= 6, so 6 are about women. Choice (B) is the credited
response.
4. E If t2 = 16, take the square root of both sides to get t = 4.
The value of t could also be –4, but the question states that t
is positive. Now, plug t = 4 into the equation (t – 1)2,
which is (4 – 1)2 = (3)2 = 9. Choice (E) is the credited
response.
5. C Translate the English into math. If a + 3a < 5b + (–b),
then 4a < 4b. Divide both sides by 4, so a < b, and (C) is
the credited response. Plugging in numbers for a and b

would also work, as long as the sum of a and 3a is less than
the sum of 5b and –b. Try a = 2 and b = 3. a + 3a = 2 +
6 = 8. 5b + (–b) = 15 + (–3) = 12. 8 < 12, which fits
the requirement in the question. Therefore, (A), (B), (D),
and (E) can be eliminated.
6. A For average problems, draw an average pie. Set A has 3
numbers and an average of 4. Put those numbers in the
lower left and lower right spots, respectively, as shown
below. To get the total, multiply 3 by 4, which is 12.

Therefore, 1 + t + 7 = 12, t + 8 = 12, and t = 4. Now,
plug t = 4 into set B. The total of set B is 2 + 4 + 6 = 12.
Draw another average pie, filling in the total and the
number of things.

Total ÷ number of things = average, so 12 ¸ 3 = 4.

Therefore, choice (A) is the credited response.
7. B When the question asks for a specific value, use PITA. For

choice (C), p = 6.
=
=
= 9.54.
This value is more than the 9 in the equation, so (C) can be
eliminated. Choices (D) and (E) are even larger than 6 and
will yield answers larger than 9.54, so (D) and (E) can be
eliminated as well. For choice (B), p = 5.
=
=
= 8.94. This is very close to 9, so (B) is
the credited response.

8. C For coordinate geometry questions, start with a sketch of
the given information. Now, sketch in the location of point
H. It will be above point G, with a negative x-coordinate
and a positive y-coordinate, as shown below.

Based on the sketch, (A), (B), and (E) can be eliminated, as
those are not in the correct quadrant. Point F is 3 units
below the x-axis, so point H will be 3 units above the x-axis.
Therefore, (C) is the credited response.
9. D The chart contains a lot of numbers with weird fractions, so

start by ballparking. If the women’s ring diameter is 16 , it
is larger than 16 , so (A) and (B) can be eliminated. Now,
rather than try to find a common denominator for all these
fractions, convert each remaining number into decimals.
The given value of 16

equals 16.75. Size 6 in (C) goes

from 16 , which equals 16.5, to 16 , which equals 16.67.
The given 16.75 is outside this range, so (C) can be
eliminated. Size 6

in (D) goes from 16.67 to 16 , which

equals 16.83. The given 16.75 is in this range, so (D) is the
credited response.
10. D With variables in the question, the best approach is to Plug
In. PITA would mean a lot of algebraic manipulation to
solve the equation for x. To answer this question, it is easier
to plug in integer values of x. If x = 1, y =

= 0.

This is not one of the fractions in the answer choices, so try
the next integer value for x. If x = 2, y =

. This is

also not one of the fractions in the answer choices, so keep
going until one works. If x = 3, y =
=

=

. If x = 4, y =

=

= . If x = 4, y
. This is the value in

(D), making (D) the credited response.
11. A When given ranges for variables but not actual values, plug
in some numbers. If p = 5 and q = 11, p + q = 5 + 11 =
16, which is less than 18. Since case I is true for these
numbers, it cannot be eliminated at this point. q – p = 11 –
5 = 6, which is not less than 6. Therefore, case II is false,
and (B) and (D) can be eliminated. 2p = 2(5) = 10, which
is not equal to 11. Therefore, case III is false, and (C) and
(E) can be eliminated. Choice (A) is the credited response.
12. D If line a is parallel to line b, then the big angle created by
the intersection of lines b and d will be equal to r°, which
equals 140°. There are 180° in a line, so the big angle and
the small angle formed by this intersection must add up to
180°. Thus, the angle in the lower left of the triangle equals
40°, since 180 – 140 = 40. There are 180° in a triangle, so
40 + 90 + s = 180. Therefore, s equals 50°, and (D) is the
credited response.
13. E This question seems like a good candidate for PITA, since it
is asking for a specific value. However, the total is based on
three different kinds of blocks, the numbers for which are
based on other quantities. Therefore, start plugging in
different values for the number of red blocks. If there is
only 1 red block, there will be 4 yellow blocks, as the
number of yellow is 3 more than the number of red. There
are 2 times as many blue as yellow blocks, so there will be
8 blue blocks. The total number of blocks equals 1 + 4 + 8
= 13. This is the smallest possible total, so (A) and (B) can
be eliminated, since they are less than 13. If there are 2 red
blocks, there will be 5 yellow blocks and 10 blue blocks.
The total number of blocks equals 2 + 5 + 10 = 17, so (E)
is the credited response.

14. E For multiple functions, plug the x-value given into the
correct function. For this problem, that means k(4) =
(j(4))3. Now, bring in the other function, plugging in the
same x-value, to get k(4) = (j(4))3 = (
+ 1)3. This
equals (2 + 1)3 = 33, so k(4) = 27 and (E) is the credited
response.
15. A The chart indicates that 20 percent of the businesses in
town are clothing stores, and the question states that there
are 100 clothing stores. Use this information to calculate
the total number of businesses in town. 100 =

× Total.

Solve this equation for the total by multiplying both sides
by

, yielding a total of 500 businesses. Now use this

total to calculate the number of bookstores and jewelry
stores. For bookstores, the number equals
For jewelry stores, the number equals

× 500 = 35.
× 500 = 25.

The difference between the two numbers is 10, so (A) is the
credited response.
16. D With variables in the answer choices, Plug In. If m = 3 and
n = 5, point A is at (3, 10) and point B is at (6, 20). The
slope can be found with any two points, and the slope

formula is

. The slope of this line is

or

.

Plug m and n into the given in the answer choices to see
which one has a slope equal to. Choice (A) is y = x, which
has the wrong slope, so it can be eliminated. Choice (B) is y
= x, so it can be eliminated. Choice (C) is y = x + 3
and can be eliminated. Choice (D) is y =

x and (E) is y =

x + 5. A quick sketch of the two points and the line
containing them will show that it goes through the origin.
Therefore, there should be no y-intercept and the credited
response is (D). Another option would be to plug one of the
points, such as (3, 10), into the two remaining equations.
Choice (D) becomes 10 =

(3), which is true and the

credited response. Choice (E) becomes 10 =

(3) + 5,

which is false, so (E) can be eliminated.
17. C This is a logic question, so check each statement to
determine if it is necessarily true about the shoes. Case I

states that if a shoe is not black, then it is not a boot. The
question only stated that boots were all black, but there
could be other black shoes, such as sandals or sneakers.
Therefore, I is not necessarily true, so (A) and (D) can be
eliminated. Case II has the same problem – other types of
shoes could also be black. Therefore, (B) and (E) can be
eliminated. Only case III is true, so (C) is the credited
response.
18. C The volume of a cylinder is the product of the area of the
circular bottom, A = πr2, and the height, h, so V = πr2h.
Given the variable d for the diameter of one ball, plug in a
number for d, such as d = 4. Therefore, the radius of the
cylinder is 2. The height is made up of three balls, or 3d, so
the height is 12. Plug these values into the formula for
volume, which yields π(22)(12) = 48π, the target number.
Now plug d = 4 into the answer choices to see which is
equal to the target number. Choice (A) is 16π, which is not
equal to 48π, so (A) can be eliminated. Choice (B) is 2π(16)
or 32π and can also be eliminated. Choice (C) is

π(64) or

48π, which is the target answer. Check out (D) and (E) to
make sure they can be eliminated. Choice (D) is 64π and
(E) is 3π(64) or 192π. Both of these can be eliminated, so
(C) is the credited response.

19. B The best way to tackle this problem is to just start listing
out numbers that fit the requirements, since the greatest
possible number of choices from the answers is 24. It is
important to be systematic, though, so no numbers that
work are left off the list. For the hundreds place, the
number must be a 7, and the tens place must be a 1. The
last digit must be a prime number, so it could be 2, 3, 5, or
7. There must be at least one 2 in the number, so start by
assuming that the last digit is 2.
Since there is now a 2 in the 4-digit number, the first digit
can be any number 1 through 9. The 4-digit numbers that
fit the requirements in this scenario are 1,712; 3,712;
4,712; 5,712; 6,712; 7,712; 8,712; and 9,712.
If the last digit was not a 2, then the first digit must be a 2.
Since there is now a 2 in the 4-digit number, the last digit
can be any of the three remaining prime numbers – 3, 5, or
7. The 4-digit numbers that fit the requirements in this
scenario are 2,713; 2,715; and 2,717. With 8 options in the
first scenario and 3 options in the second, there are 11 total
possible numbers, so (B) is the credited response.
20. E Given a geometry problem with no figure, draw one. The
question states that side
is shorter than the other two
sides. So draw an isosceles triangle with a base slightly
shorter than the two equal legs, as shown below.

Now, with a picture for reference, it is time to PITA. Choice
(C) gives a measure of 50° for ∠T . This will also be the
measure for ∠U, since isosceles triangles have two equal
angles. There are 180° in a triangle, so there are 80° left for
∠V. This makes ∠V larger than the other two angles, so
side
would be longer than the other two sides.
Therefore, (C) can be eliminated. Since ∠V needs to be
smaller, ∠T and ∠U need to be larger, so (A) and (B) can
also be eliminated. Choice (D) makes ∠T equal to 60°, so
∠U equals 60°, and there are 60° left for ∠V. The sides are
all equal now, so
still is not shorter than the other sides.
Choice (D) can be eliminated, and (E) is the credited
response.

Section 4
21. A In the first equation, subtract 3 from both sides to find that
p = 9. Plug in 9 for p in the second equation: 9 – q = 5.
Subtract 9 from both sides of the equation, then divide by –
1 to find that q = 4. The credited response is (A).
22. E First, list out the numbers in each set. For sets A and B, only
list up to the highest answer choice, in this case 18. Set A =
{2, 4, 6, 8, 10, 12, 14, 16, 18, …}. Set B = {9, 18, …}. Set
C = {1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60}. Now check the
answers to see which number is a member of both sets A
and B, but not of set C. 6 is in all three sets, so eliminate
(A). 9 is only in set B, so eliminate (B). 12 is in sets A and
C, but not in set B, so eliminate (C). 15 is only in set C, so
eliminate (D). 18 is in both sets A and B but not in set C, so
the credited response is (E).
23. C Make sure to read the labels on the axis of the chart. Draw a
vertical line at the 25 minute mark, then draw a horizontal
line at the 400 calories mark. Count the number of dots that
are above and to the right of where those two lines meet.
There are four dots. The credited response is (C).
24. E Start by drawing the point (3, 8). Then draw line p
perpendicular to line m through point (3, 8). Use your eye
to determine where the lines intersect. All the points on line
m have a y value of 5 and all the points on line p have an x
value of 3. The lines will cross at point (3, 5). The credited
response is (E).
25. E Geometry basics: Draw, Label, Formulas. The figure is
drawn already. The triangle is equilateral so all of the sides

are the same. Since the perimeter is 54, divide that by three
to find the sides of the triangle are 18. Label the sides in the
figure. To find circumference of the circle, write the
circumference formula: C = πd. Notice that the side of the
triangle is the diameter of the circle, so the diameter of the
circle is also 18. Put that into the formula: C = 18π. The
credited response is (E).
26. B “What is the value” with numbers in the answers … PITA!
Normally you should start with choice (C) because it’s in
the middle, but it’s an ugly number. It will be easier to start
with (B) because it’s a whole number. The question asks for
x so start with choice (B) and plug in –1 for x. If x = –1
then each tick mark is , which makes y =
Plug y and z into the equation to check.

+

and z =
=

.

= 2,

which matches the question. The credited response is (B).
27. A Variables in the question and the answer choices: Plug In!
Remember that t is in years and that the number of hit
records doubles every 6 months. Let’s plug in 3 for t, which
means that the number of hit records will double 6 times.
Starting with 1 hit record, it doubles to 2 (6 months), then
doubles to 4 (one year), then doubles to 8 (1 year 6
months), then doubles to 16 (2 years), then doubles to 32 (2
years 6 months), then doubles to 64 (3 years). So when t =
3, the target is 64. Plug 3 into each of the answer choices.
Choice (A) is 22×3 = 26 = 64, which matches the target.
Remember to check all of the answers to be safe. The
credited response is (A).

28. D Since the parabola is symmetrical across the line x = −1 ,
the x-intercepts are equidistant from the point (−1 , 0).
First find the distance from (−1 , 0) to (–5, 0) by
subtracting the x-coordinates: −1 − (−5) =

+

=

. The other x-coordinate is the same distance from (−1 ,
0), so add
−

=

to find the other x-coordinate:

+ (−1 ) =

= 2 . The other x-intercept is (2 , 0), so m =

2 . The credited response is (D).
29. 4 Since each term is three times the previous term, y × 3 =
36 and, thus, y = 12. Then, x × 3 = 12, and, thus, x = 4.
30. 40 It’s safest to use the calculator on this question. Make sure
to either do it in small steps and correct order of operations
(PEMDAS) or be careful when typing the parentheses. To
solve, plug in 15 for m in the equation: P(m) = 125,000
= 125,000

= 125,000

= 40.

31. 105 All the angles in a square are 90°. Since the small angle at
point C is 15°, the large angle above it must be 90 – 15 =
75. All straight lines have 180°, so 75 + y = 180. Subtract
75 from both sides of the equation to find that y = 105.

32. 15 Recognize that the problem gives a relationship and a total
value. Set up the ratio box. The actual total number of
marbles is 40, so write that in the bottom right box.
Probability is a “part to whole” relationship; on the Ratio
row, write 5 for red and 8 for total.

The Ratio row adds across, so write 3 for blue. Find that the
multiplier from 8 to 40 is 5, which is the same multiplier
for everything. Multiply to find that there are 25 red
marbles and 15 blue marbles. The question asked for blue,
so the answer is 15.

33. 20 Geometry basics: Draw, Label, Formulas. There’s no figure,
so draw the two triangles. Then write the area formula: A
=

bh. The problem provides the area but neither the base

nor height, so Plug In! For triangle A write 120 =

bh, so

bh = 240. Plug in numbers that work, such as b = 12 and h
= 20. Since the base of triangle A is three times that of
triangle B, divide the base of triangle A by 3 to get

= 4.

Since the height of triangle A is two times that of triangle B,
divide the height of triangle A by 2 to get

= 10. Now

use the area formula again with the numbers of triangle B
to find A =

bh =

(4)(10) = 20.

34. 13 Translate the English to Math. First translate “Sue and David
together own 57 hamsters” to “s + d = 57”. “David owns”
translates to “d =”, “5 more than” translates to “5 +”, and
“3 times the number of hamsters that Sue owns” translates
to “3 × s”. Put it together to get d = 5 + 3s. Now
substitute 5 + 3s for d in the first equation to get s + (5 +
3s) = 57. Simplify and solve: 4s + 5 = 57, then 4s = 52,
then s = 13. Sue owns 13 hamsters.
35.

Definition: “bisects” means “cuts in half.” Since there are no
numbers given, Plug In! Starting with the first given angle,
plug in 40 for ∠COG. Since
and ∠EOG are 20. If

bisects ∠COG, both ∠COE

bisects ∠AOE then ∠AOC and

∠COE are equal, so they are both 20. If

bisects ∠AOC

then ∠AOB and ∠BOC are equal, so they both equal 10. If
bisects ∠EOG then ∠EOF and ∠FOG are equal, so they
both equal 10. Add the angles to find that ∠COG = 40 and
∠AOF = 50. Therefore
36.

0<n<1

.

This question is testing properties of number and exponents.
Plug In to test what happens to different types of numbers.
Try 1 first, because it’s easy. The reciprocal of 1 is 1 and 12
= 1. The reciprocal and the square of 1 are equal; neither is
greater than the other so 1 is not a possible value. Now try
something greater than 1, such as 3. The reciprocal of 3 is
and 32 = 9. Since

is not greater than 9, this is not a

possible value. Notice that the reciprocal got smaller and
the square got bigger than the original number. This will be
true for all numbers greater than 1. Now try again with a
fraction less than 1, such as
( )2 =

. The reciprocal of

. Since 4 is greater than

,

is 4 and

is one possible

value. Any fraction between 0 and 1 will work. The
reciprocal of a fraction between 0 and 1 will be greater than
1, and the square of a fraction between 0 and 1 will be a
smaller fraction.
37. 187 This is a pattern question. Doing the quick calculation will
likely lead to a trap answer. Be careful and list out the
pattern. There are five pages in each section, so list 1, 2, 3,
4, 5. Then list the page numbers of each section. To save a
little time, recognize the pattern. The last page of each
section is 5 more than the last page of the previous section,
so continue to add 5 until section 7. The last page is 187.

38.

or 0.185
Variables! Plug In! The easiest numbers to choose are r = 5
and s = 6. Then plug s = 6 into the second equation to get
. Solve to find that t = 27. Therefore

.

Section 5
1. C The phrase An opener for 1999’s “Geniuses, Savants, and
Prodigies” conference is a modifying phrase, so whatever
comes immediately after the comma must be the person or
thing described in the phrase. Since the piano did not serve
as an opener, the original sentence contains a misplaced
modifier. David Helfgott was the person who was an opener,
so his name should appear immediately after the comma.
Eliminate both choices (A) and (B). Choices (D) and (E)
both place David Helfgott immediately after the comma, but
because they use the word who, they both create incomplete
sentences. Only choice (C) correctly fixes the misplaced
modifier and does not introduce any new errors.
2. E If you trim the fat and eliminate the descriptive phrase a
flightless dodo bird once native to the island of Mauritius,
you’re left with The dodo bird … that was being discovered in
1958. The original sentence is incomplete, since the phrase
that was being discovered in 1958 serves as a descriptive
phrase and does not contain a main verb. Choices (A), (B),
(C), and (D) all repeat the original error since none of them
turn the sentence into a complete thought. Only choice (E)
fixes the error in the original sentence.
3. B The second half of the sentence needs to modify the first
half. As it’s currently written, the second half of the
sentence does not clearly state what did the initiating, and
therefore does not modify the first half of the sentence.
Eliminate choice (A). Choice (B) correctly modifies the first
half of the sentence, and it contains no additional errors.
Choices (C) and (E) both turn the second half of the
sentence into complete thoughts. Since the first half of the

sentence is also a complete thought, both choices (C) and
(E) create comma splices, so eliminate them. Choice (D) is
wordy and does not fix the error in the original sentence.
The correct answer is (B).
4. B The phrase Determined to finish the game despite the rain is a
modifying phrase that must describe whatever appears
immediately after the comma. Since the football team, and
not the football team’s fight, was determined, this sentence
contains a misplaced modifier. Choices (A) and (E) repeat
this error. Choices (C) and (D) also contain misplaced
modifiers, since these choices make it seem as though the
trophy, not the football team, was determined. Choice (B)
fixes the error and does not introduce any new errors, so it
is the correct answer.
5. D The original sentence uses the word being. Whenever
possible, avoid choosing answers that use being, so
eliminate choices (A) and (C). Choice (B) creates a fragment
and unnecessarily uses the word they. Choice (D) does not
use the word being and does not introduce any new errors,
so choice (D) is the correct answer. Choice (E) removes the
verb are and replaces it with as. Without the main verb, the
sentence is incomplete, so choice (E) is not the correct
answer.
6. B As the sentence is currently written, the phrase an aweinspiring and enormous painting that covers nearly 650 square
feet modifies Jacques-Luis David. However, since The
Coronation of Napoleon, not David, is a painting, the
sentence contains a misplaced modifier. Choice (E) repeats
this error, so you can eliminate choices (A) and (E). Choice
(B) fixes the error by adding the verb is, so that the second
half of the sentence is no longer a modifying phrase. The
verb is refers back to The Coronation of Napoleon, so the
intended meaning of the sentence is now clear. This choice

does not introduce any new errors, so choice (B) is the
correct answer.
7. E As the sentence is currently written, the new phone is the
subject of the verb deducting. However, since the phone is
not the person or thing doing the deducting, the sentence is
incorrect as written, and you can eliminate choice (A).
Choice (C) changes the meaning of the sentence by
implying that the cost was somehow a fraction of the
deduction, and is therefore incorrect. Choices (B) and (D)
both use –ing verbs, whereas choice (E) does not. If
possible, you generally want to eliminate –ing verbs, so
choice (E) is the best choice.
8. C The pronoun them does not clearly refer to any other noun
in the sentence. Therefore, this sentence contains a pronoun
ambiguity error. Choices (A), (B), and (E) repeat the
original error, and are therefore incorrect. Choice (C) is
much more concise than choice (D), and is therefore the
correct answer.
9. B This sentence incorrectly uses was needing rather than
needed. Additionally, this sentence contains two complete
thoughts joined by a comma, and is therefore a comma
splice. Eliminate choice (A). Choice (E) repeats the comma
splice error and is also incorrect. Choice (C) uses the
modifying phrase Having gone to the car dealership. This
phrase should modify whatever appears immediately after
the comma. However, the word buying appears immediately
after the comma in this case. Since the word buying cannot
go anywhere, this choice contains a misplaced modifier.
Choice (D) is passive, and incorrectly places the modifying
phrase where she needed to buy a new car immediately after
Lindsay, rather than after car dealership. Choice (B) fixes
both of the errors in the original sentence and does not
introduce any new errors, so choice (B) is the correct

answer.
10. E The pronoun they is unnecessary and turns the first half of
the sentence into a fragment. Therefore, choice (A) is
incorrect. Choice (B) changes the intended meaning of the
sentence by making it appear as though the detectives were
determined to catch the criminal simply because they
wanted to identify the criminal. Choice (D) similarly
changes the meaning. In choice (C) the clause The detectives
identified the criminal is a complete thought, and the clause
they were determined to catch the man who stole the jewelry is
also a complete thought. Since this choice joins two
complete thoughts with a comma, thus creating a comma
splice, this choice is incorrect. Choice (E) fixes the error in
the original sentence and does not introduce any new
errors, so choice (E) is the correct answer.
11. E The original sentence lists two things that employees want:
more responsibility and to increase their monthly earnings.
Since responsibility is a noun, and increase is a verb, and
these two words are in a list, the list is not parallel.
Therefore, choice (A) is incorrect. Choice (B) is passive,
since the compound subject of the sentence is more
responsibility and an increase, the verb is are wanted, and the
employees, who are the people doing the action, are not the
subject of the sentence. Choice (C) changes the meaning of
the sentence by suggesting that the reason that many
employees volunteer to work overtime is that they want
more responsibility. Choice (C) is therefore incorrect. Choice
(D) begins the sentence with while. However, this sentence
does not contain two contrasting thoughts, and thus should
not begin with while. Choice (E) fixes the error in the
original sentence and does not introduce any new errors, so
it is the correct answer.
12. C The subject of the sentence is works, which is plural, and the

verb is ranges, which is singular. Therefore, this choice has a
subject-verb agreement error. Eliminate choice (A). Choices
(B) and (E) change the verb to an –ing form and turn the
sentence into a fragment. Choice (D) adds the word that,
which would indicate that an additional thought should
come after the phrase that range from Russian ballets to
neoclassical compositions and chamber works. Choice (D)
makes the sentence incomplete, and is therefore incorrect.
Choice (C) fixes the subject-verb agreement error by making
the verb plural, so choice (C) is the correct answer.
13. A Choice (B) is disjointed and contains the word being.
Whenever possible, avoid choosing answers that include the
word being. Eliminate choice (B). Choice (D) also uses being
and is incorrect. Choice (C) uses an unnecessary and, and is
therefore a run-on. Choice (E) lists two facts about the
authors’ works: they are difficult to comprehend and
symbolizing obscures … the author’s main point. Since these
two items are not in parallel form, this choice contains a
parallelism error. Choice (A) correctly joins two complete
thoughts with a semicolon and does not contain any
additional errors. Choice (A) is the correct answer.
14. D In the original sentence, being banned is an incorrect form of
the verb. Remember to avoid the word being whenever
possible. Eliminate choice (A). Do not use helping verbs
such as should or have with verbs such as urge that
communicate a wish or a command. Choices (B) and (C)
both break this rule, and are therefore incorrect. Choice (E)
changes the meaning by using the phrase for initiating, thus
suggesting that the league suggested the ban for the
purpose of initiating the movement. Choice (D) correctly
uses the subjunctive voice, stating that the Anti-Saloon
League urged that the sale … be banned. Choice (D) is the
correct answer.

15. D The clause Charlemagne was crowned in 768 A.D. as King of the
Franks is a complete thought. The clause he was the oldest
son of Pepin the Short and Bertrada of Laon is also a complete
thought. Since this sentence links two complete ideas with a
comma, this sentence contains a comma splice error.
Eliminate choice (A). Choice (E) repeats this type of error
by setting the complete thought in 768 A.D. he was crowned
King of the Franks off by commas. Choice (B) uses the
pronoun they, which does not clearly refer to any group of
people mentioned in the sentence, and is therefore incorrect
(C) uses a comma followed by the word and, and should
therefore link two complete thoughts. However, since the
first half of the sentence is a fragment, choice (C) is
incorrect. Choice (D) fixes the original error in the sentence
and does not introduce any new errors, so choice (D) is the
correct answer.
16. B The singular pronoun it refers to the plural noun bulbs, so
the original sentence has a pronoun agreement error.
Choices (A) and (E) repeat the original error and thus are
incorrect. Choice (C) turns the sentence into an incomplete
thought and is therefore incorrect. Choice (D) uses the
plural pronoun their to refer to the singular noun bulb, so
choice (D) has a pronoun agreement error. Choice (B) fixes
the error, and does not introduce any new errors, so choice
(B) is the correct answer.
17. D This sentence uses the word consider twice, and therefore
has a redundancy error. Choices (A) and (C) repeat this
error, and are therefore incorrect. Choice (B) redundantly
uses the word it, and is therefore incorrect Since
consider … as to be is the wrong idiom, choice (E) is
incorrect. Choice (D) fixes the original error in the sentence,
and does not introduce any new errors, so choice (D) is the
correct answer.

18. D The original sentence uses the conjunction and, therefore
making the sentence incomplete. Eliminate choice (A).
Choices (B) and (C) inappropriately change the verb to
would create. They both also compare Hemingway’s writing
style to any other American writer. Since writing styles should
be compared to other writing styles, rather that writing
styles to writers, both of these choices also contain
comparison errors. Choice (E) changes was different to was
differing, and therefore uses the wrong form. Choice (D)
corrects the error in the original sentence and does not
introduce any new errors, so choice (D) is the correct
answer.
19. C According to the sentence, crusaders did two things: they
succeeded not in gaining access … but to leave. Since gaining
and to leave are not in the same verb form, this sentence
contains a parallelism error. Choices (A), (B), (D), and (E)
all contain similar parallelism errors, and are therefore
incorrect. Only choice (C) fixes the original error and does
not introduce any new errors.
20. D In the original sentence, the subject is reputations, which is
plural, but the verb is appears, which is singular. Therefore,
this sentence contains a subject-verb agreement issue.
Eliminate choice (A). Choice (B) changes the subject of the
sentence to either, which is singular, but it later replaces
either with the pronoun their, which is plural, so choice (B)
is incorrect. Choice (C) uses the singular subject either, but
changes the verb to appear, which is plural, so choice (C) is
not the credited answer. Choice (E) does fix the original
error but is written in passive voice. Choice (D) is the
correct answer.
21. C Choice (C) contains two errors. First, this sentence uses
between … or. The correct idiom is between … and.
Therefore, this sentence contains an idiom error. Second,

this sentence contains a parallelism error. There are two
things Abigail must choose between: the upscale bistro and
eating at the diner. In a correct version, Abigail can either
choose between eating at the upscale bistro and eating at
the diner, or she can choose between the upscale bistro and
the diner, but she cannot choose between a bistro (a thing)
and eating (an action).
22. D The subject of the sentence is each, which is singular.
However, this sentence uses the pronoun they, which is
plural, to replace the singular subject each. Thus, this
sentence contains a pronoun agreement error. Additionally,
since the pronoun should be the singular he or she, the verb
find, which is plural, should be finds, which is singular.
Choice (D) therefore contains two errors and is the correct
answer.
23. C If you use the phrase not only, you must include the words
but also later in the sentence. However, this sentence
instead uses and also, and therefore contains an idiom error.
Thus, choice (C) is the correct answer.
24. B In this sentence, the adjective reputed modifies the adjective
safe. However, an adverb, not another adjective, should
modify an adjective, so the sentence should say that the
outlaws committed crimes in a reputedly safe part of the
country. Choice (B) therefore contains an error and is the
correct answer.
25. A Choice (A) contains an idiom error, since the verb asserted
should not be paired with the preposition on. Correctly
written, the sentence should say that Descartes confidently
asserted his ability.
26. B The pronoun they is plural, but refers to the noun chef,
which is singular, so choice (B) contains a pronoun

agreement error. The correct answer is choice (B).
27. C The verb is is singular, but the subject of the verb is the
plural noun tenants. Therefore choice (C) contains a subjectverb agreement error, which makes it the correct answer.
28. E The verb argued in choice (A) is in past tense and agrees
with the subject, so there is no error in choice (A). In choice
(B), many of them correctly refers back to those those
convicted, so you can eliminate choice (B). Choice (C) uses
the correct preposition and is therefore not the correct
answer. Choice (D) properly pairs either with the
conjunction or, so choice (D) does not contain an error.
There are no errors in this sentence, so the correct answer is
(E).
29. B This sentence begins by using the pronoun you, but later
incorrectly replaces that pronoun with one, rather than you.
Thus, choice (B) is the correct answer.
30. B Choice (B) uses the present perfect verb have attempted. The
present perfect tense indicates that an action began in the
past, and is still continuing today. However, the sentence
indicates that the action occurred in 1990. Since the action
occurred at one definite point in the past, the verb have
attempted is in the wrong tense and should be in the simple
past tense. Thus, choice (B) contains an error and is the
correct answer.
31. E Choice (A) correctly begins a modifier which describes cave
paintings. Because paintings is plural, many of which agrees in
number with paintings. The plural verb are in choice (B)
agrees with the plural noun paintings, so choice (B) can be
eliminated. Choice (C) correctly uses a plural noun,
remnants, to refer back to the paintings, so you can eliminate
choice (C). Choice (D) has no errors in verb tense. Because

the sentence is correct as written, choice (E) is the correct
answer.
32. A In a sentence which uses the pairing neither … nor, the verb
must agree with the last element in the list. In this case, the
last element in the list is team, which is singular. However,
the verb were is plural, so choice (A) contains a subject-verb
agreement error.
33. C Choice (C) uses the plural pronoun them to refer to the
singular noun cloud. Therefore, choice (C) contains a
grammatical error and is the correct answer.
34. D This sentence compares two things: the game of Go and chess
pieces. However, in order for the comparison to be parallel,
the sentence must either compare the game of Go and the
game of chess, or it must compare Go pieces and chess pieces.
Therefore choice (D) contains a comparison error and is the
correct answer.
35. B This sentence uses the verb is compelling, which is in a tense
that indicates continuous action. However, since this
sentence discusses an action that should happen only once,
rather than on a continuous basis, this sentence contains a
verb tense error. Eliminate choice (A). Choice (C) changes
the intended meaning of the sentence by suggesting that
some form of tragedy must befall the people discussed in
the sentence, so choice (C) is incorrect. Choice (D)
incorrectly uses the pronoun you to refer to the people
mentioned in the previous sentence, and thus contains a
pronoun agreement error. Choice (E) uses the singular noun
person to refer to the noun people, which is plural, so choice
(E) contains a noun agreement error. Choice (B) fixes the
error in the original sentence and does not introduce any
new errors, so choice (B) is the correct answer.

36. B Choice (A) combines the two sentences, but the conjunction
and does not correctly connect the two thoughts since they
are not directly related. Choice (B) is more concise than
choice (A), and correctly joins the two sentences without
introducing any new errors. Choice (C) connects the two
thoughts using a semicolon. However, a semicolon should
connect two complete thoughts. In this case, the first part of
the sentence, which reads, The story of the poor London boy
Tom Canty, which demonstrates the lesson is not a complete
thought. Therefore, Choice (C) contains an error and is not
the correct answer. Choice (D) changes the intended
meaning of the sentence by placing the phrase a poor boy
from London immediately after Mark Twain, thus suggesting
that Mark Twain, not Tom Canty, was the poor boy from
London. Additionally, this sentence contains two complete
thoughts joined by a comma, and thus contains a comma
splice error. Choice (E) places the modifying phrase
demonstrating the lesson through the story of poor London boy
Tom Canty at the end of the sentence. This sentence changes
the meaning so that it is unclear exactly what is
demonstrating the lesson, and therefore contains a
misplaced modifier error. Choice (B) is the only answer
remaining and is therefore correct.
37. A The end of the second paragraph discusses the fact that Tom
learns to appreciate the things that he does have, rather
than envying what others have. However, the paragraph
does not really explain how Tom learns this lesson, merely
stating that life in the prince’s court was more complicated
than he had anticipated. Therefore, the author could
strengthen his or her point by including more details about
what caused Tom to miss and gain such appreciation for his
home in London. Choice (A) correctly identifies the pieces
of information missing from the second paragraph, and is
the correct answer. While adding information about the

ways in which the customs in Prince Edward’s court were
intricate might be helpful, the ways in which those customs
relate to the customs in other courts is irrelevant to the
topic. Therefore, choice (B) is not the correct answer. The
paragraph and the essay as a whole do not relate to the
reasons that Tom’s family became poverty-stricken, but
instead relate to how Tom learned to appreciate his life
despite that poverty. Thus, choice (C) is not the correct
answer. The second paragraph does relate to how Tom
gained an appreciation for his home in London, but it does
not relate to the literary devices that Mark Twain used to
convey that lesson. Eliminate choice (D). Finally, the second
paragraph focuses on Tom, rather than Mark Twain, so a
discussion of Twain’s life would be out of place at this point
in the essay. Therefore choice (E) is incorrect.
38. E Choice (A) uses the singular pronoun one to replace the
plural pronoun they, and therefore contains a pronoun
agreement error. Both choices (B) and (C) inappropriately
change the pronoun in the sentence to you, rather than they.
Since the pronoun refers to many people, the pronoun you is
incorrect, so you can eliminate choices (B) and (C). Choice
(D) changes the present tense verb fail to the past perfect
verb have failed. Since the rest of the verbs in the sentence
are in the present tense, and the sentence does not call for a
tense change, this choice contains a verb tense error. Choice
(E) correctly joins the two sentences and does not introduce
any new errors, so choice (E) is the correct answer.
39. E Sentence 3 provides a transition from the main topic of the
essay to the example of The Prince and the Pauper and is
therefore an important part of the first paragraph. Without
sentence 4, readers would not know which book the author
is discussing, so sentence 4 is also a critical part of the first
paragraph. Sentence 8 demonstrates how the example of

The Prince and the Pauper relates to the main topic of the
essay, and is therefore necessary to the essay. Sentence 9
relates the example of the book back to the essay’s thesis by
showing how the example relates to people in general.
Therefore, sentence 9 should remain in the essay. Sentence
10 links the idea in sentence 9 to the idea in sentence 12,
and is therefore a valuable part of the essay. However,
sentence 11 introduces irrelevant information. The previous
sentence discusses the idea that it is possible to appreciate
those who love us before we lose them, and the sentence
that follows discusses the idea that few people actually
learn this lesson before it is too late. Thus, sentences 10 and
12 discuss related ideas, but sentence 11, which points out
that many believe that Tom is a more engaging character
than Prince Edward, provides unnecessary information. The
correct answer is choice (E).

Part IV
Practice Tests

Chapter 7
Practice Test 2

SECTION 1
Time — 25 minutes
24 Questions
(1–24)
Directions: For each question in this section, select the best answer from among the
choices given and fill in the corresponding circle on the answer sheet.

Each sentence below has one or two blanks, each blank indicating that something has
been omitted. Beneath the sentence are five words or sets of words labeled A through
E. Choose the word or set of words that, when inserted in the sentence, best fits the
meaning of the sentence as a whole.
Example:

Desiring to ------- his taunting friends, Mitch gave them taffy in hopes it would keep
their mouths shut.

(A) eliminate (B) satisfy (C) overcome (D) ridicule (E) silence

1. Since the coach didn’t want the opposing team to pick up her signals to the
runner, she was careful to use the utmost -------.

(A) athleticism (B) discretion (C) autonomy (D) credibility
(E) disparity

2. Recently unearthed drawings of spears, traps, and cudgels from ancient times

2. Recently unearthed drawings of spears, traps, and cudgels from ancient times
show that ------- was necessary for each head of the household, thus making
him the ------- of the provider of the family.
(A) sporting . . epicenter
(B) farming . . highlight
(C) hunting . . embodiment
(D) fishing . . enemy
(E) running . . epitome
3. Hall of Fame baseball player Ty Cobb’s skills as an athlete have never been
questioned by those with knowledge of the game, even if his personal

temperament has never been agreed upon: his few instances of kindness and
generosity are often ------- by stories of uncontrollable -------.
(A) highlighted . . irritability
(B) rebutted . . charity
(C) contradicted . . jealousy
(D) overshadowed … irascibility
(E) bequeathed . . ecstasy
4. The celebrity chef believed that originality was a far better attribute of good
cooking than mere skill, consistently stating that diners much prefer ------over -------.

(A) innovation . . competence
(B) enigma . . concord
(C) novelty . . opulence
(D) revolution . . craft
(E) decadence . . mendacity

5. In contrast to what Ms. Banks expected from her students, Raphael was always

5. In contrast to what Ms. Banks expected from her students, Raphael was always
------- instead of punctual, and consistently disrespectful when he should have
been -------.

(A) mercurial . . grandiose
(B) sluggish . . dutiful
(C) tardy . . deferential
(D) dilatory . . ornery
(E) meticulous . . obedient
6. Rupert criticized the new film as too much of -------: it highlighted the origins

of the story’s characters without fully realizing their motivations or coming to
a satisfying resolution.

(A) a prelude (B) a picaresque (C) a roman a clef (D) an anachronism
(E) an epilogue

7. The films of the 1980s were considered clichéd and commercial, as opposed to
those of the 1970s that were remembered as ------- and -------.
(A) conventional . . derogatory
(B) maverick . . ubiquitous
(C) cinematic . . nonsalable
(D) therapeutic . . superfluous
(E) iconoclastic . . independent
8. The auto mechanic’s ability to diagnose a vehicle’s problem prior to inspection
prompted his customers to describe him as -------.

(A) prescient (B) efficient (C) vicarious (D) scintillating (E) precocious

The passages below are followed by questions based on their content; questions

following a pair of related passages may also be based on the relationship between the

paired passages. Answer the questions on the basis of what is stated or implied in the
passage and in any introductory material that may be provided.
Questions 9-10 are based on the following passage.

9. The author uses the phrases “kill the chicken” and “drop the food” (line 9) in
order to

(A) emphasize the urgency for Samuel to learn English
(B) underscore the silliness in restaurant lingo
(C) highlight the benefits of Samuel’s gradual integration of the English
language

(D) criticize Samuel’s inability to write a full English letter
(E) show Samuel’s fascination with the restaurant industry

10. The passage indicates that Samuel’s limited familiarity with English was

10. The passage indicates that Samuel’s limited familiarity with English was
considered

(A) advantageous
(B) debilitating
(C) satisfying
(D) humbling
(E) appetizing

Questions 11-12 are based on the following passage.

11. The author mentions “candies” and “breads” in lines 4-5 in order to
(A) show items that are commonly associated with sugar
(B) indicate the range of items that contain sugar
(C) caution against overfeeding children with sugar products
(D) argue that sugar is an ingredient in far too many foods
(E) criticize the use of sugar in abnormal foods
12. The passage suggests which of the following about sugar?
(A) It rivals illegal narcotics as the most addictive substance consumed by
humans

(B) Rats and humans process sugar in the same way
(C) It is more prevalent in foods today than it was ten years ago
(D) It is an ingredient in most food products today
(E) People are sometimes powerless to avoid consuming sugar products

Questions 13-24 are based on the following passage.
This passage is adapted from a 2009 book looking at Western (that is, European and
American) attempts to modernize the Middle East and other regions.

13. In the context of lines 1-3 (“The international … East”), the phrase
“overflowing with” suggests that

(A) modernization is a common subject of conversation for Middle Eastern
visitors to the West

(B) some Middle East countries have been subject to more modernization
efforts than others

(C) there have been many attempts by Western countries to modernize the
Middle East

(D) there are simply too many countries in the Middle East for historians to
describe accurately

(E) the Middle East is a populous region with a rich historical legacy

14. The author mentions Bill Clinton (line 6) primarily in order to

14. The author mentions Bill Clinton (line 6) primarily in order to
(A) cite one person who represents a certain perspective
(B) describe the rewards of one person’s courage against difficult odds
(C) state that those who have contributed to peace in the region come from
a variety of backgrounds

(D) show that Middle East peace was only one of Clinton’s minor
accomplishments

(E) argue that this approach to Middle East issues is the correct one
15. According to the passage, it is worth asking “whether Western systems of
government are universally applicable” (lines 16-17) because they

(A) are too reliant upon ancient forms of non-Western government
(B) refuse to recognize the accomplishments of diplomats like Bill Clinton
(C) have as their only goal the introduction of Western goods into nonWestern markets

(D) may not be the most appropriate forms of government for those outside
the West

(E) deny the importance of having native peoples in high government
positions

16. Which of the following best states how the peoples mentioned in line 31 feel
about West-influenced governments?

(A) They despise the governments because they are hopelessly corrupt.
(B) They question the ability of their fellow citizens to govern them.
(C) They disagree with how local money is being paid out to officials.
(D) They doubt that the governments have delivered on all that they have
promised.

(E) They support the new regime because it represents a change from old
ways.

17. According to the author, what has changed “since the seventeenth century”
(lines 34-35)?

(A) Native citizens are now in open conflict with Western-style
governments.

(B) Middle Eastern government officials look to the West for models of how
to govern.

(C) Regions that were once considered model civilizations are no longer
thought of as ideals.

(D) People in non-Western countries are not willing to compromise in a way
that supports democracy.

(E) Those who were once unable to govern themselves have been helped by
those who have shown them how to govern.

18. The statement that Western influence “has not been a pure force for good”
(line 47) suggests that the author, in general, believes that

(A) people in the Middle East would prefer to have their fellow citizens in
high government positions

(B) people in the Middle East have not necessarily benefited from Westernstyle governments

(C) voters in Middle East elections wish there were more candidates from
the West

(D) forms of democracy in the Middle East are more advanced than those in
the West

(E) Western policymakers did not expect voter turnout to be as low as it has
been in Middle East elections

19. In line 58, “trumps” most nearly means

19. In line 58, “trumps” most nearly means
(A) kicks out
(B) performs
(C) defeats by force
(D) beautifies
(E) is more important than
20. In line 67, “maintain” most nearly means
(A) work
(B) repair
(C) hang
(D) sit
(E) build
21. Which of the following, if true, would refute the claim made in lines 70-71
(“As … themselves”)

(A) The Western influence in the Middle East has not been able to overcome
internal divisions among groups within Iraq.

(B) Many representatives from the Middle East have been crucial to

developing the government systems that exist in the Middle East today.

(C) Contemporary styles of government in the Middle East can be traced
back to principles developed in Europe in the late 1700s.

(D) Famous diplomats such as Bill Clinton have continued to offer guidance
to those in the Middle East and elsewhere.

(E) The U.S. has ensured that Sunnis, Shias, and Kurds are equally
represented in the Iraqi government.

22. Which of the following best describes the sentence in lines 80-81

22. Which of the following best describes the sentence in lines 80-81
(“Certainly … been”)?

(A) A response to critics of the author’s own argument
(B) An idea developed further in other work by the author
(C) A tangent that the author considers necessary for his main point
(D) A concession that contemporary trends are not exclusively negative
(E) A restatement of the author’s central claims
23. The author uses the phrase “repackaging of an old product” (line 83) primarily
to

(A) outline an analogy for an ideal approach
(B) suggest the type of reformulation necessary for success
(C) express skepticism toward a certain transformation
(D) criticize the financial interests of Western governments
(E) admit that the Western approach has many benefits
24. The author would most likely consider which approach to be a new strategy
for the formation of governments in the Middle East?

(A) Allowing Western governments to shape government policy in the
Middle East

(B) Breaking down cultural barriers within countries to promote national
unity

(C) Increasing the authority of government official to implement Western
democracy

(D) Collaborating with local representatives to determine which style of
government is best for a particular country

(E) Holding elections in the West to determine which officials should
represent Middle East governments

ST OP
If you finish before time is called, you may check your work on
this section only.
Do not turn to any other section in the test.

SECTION 2
Time — 25 minutes
20 Questions
(1-20)
Directions: For this section, solve each problem and decide which is the best of the
choices given. Fill in the corresponding circle on the answer sheet. You may use any
available space for scratchwork.

Notes
1. The use of a calculator is permitted.
2. All numbers used are real numbers.
3. Figures that accompany problems in this test are intended to provide information
useful in solving the problems. They are drawn as accurately as possible

EXCEPT when it is stated in a specific problem that the figure is not drawn to
scale. All figures lie in a plane unless other wise indicated.

4. Unless otherwise specified, the domain of any function f is assumed to be the set
of all real numbers x for which f(x) is a real number.

Reference Information

The number of degrees of arc in a circle is 360.
The sum of the measures in degrees of the angles of a triangle is 180.

1. A spice merchant sells ground cinnamon for x dollars per ounce. At this rate,

1. A spice merchant sells ground cinnamon for x dollars per ounce. At this rate,
what is the cost of 3 ounces of cinnamon, in dollars, in terms of x ?
(A)
(B)
(C)
(D) 3x
(E) 3

2. If 5.73 × 10h equals 0.0573, what is the value of h ?
(A) –2
(B) –1
(C)

1

(D)

2

(E)

3

3. If 3a = 5 and 2b = 9, what is the value of 2(3a) + 4(2b) ?
(A) 32
(B) 45
(C) 46
(D) 58
(E) 66

4. The sum of a and b is 18 and the sum of c, d, and e is 37, what is the average

4. The sum of a and b is 18 and the sum of c, d, and e is 37, what is the average
(arithmetic mean) of a, b, c, d, and e ?
(A)

8

(B) 11
(C) 18
(D) 20
(E) 22

5. In the figure above, triangles LMQ and MNO are equilateral. If LM = 2 and
MN = 3, what is the perimeter of the parallelogram MOPQ ?
(A)

3

(B)

4

(C)

5

(D)

8

(E) 10

6. If 13 – (x + y)2 = 4, which of the following could be the value of (x + y) ?

6. If 13 – (x + y)2 = 4, which of the following could be the value of (x + y) ?
(A) –
(B) –3
(C)
(D) 13
(E) 17

7. In the figure above, quadrilateral FJKL is the reflection of quadrilateral FGHJ
about the line y. What is the value of z ?
(A)

20

(B)

80

(C) 120
(D) 140
(E) 160

8. The sum of 50° and ∠p is 180°. Which of the following angles could be ∠p ?

(A)

(B)

(C)

(D)

(E)

9. If the number t is quadrupled, the result is the same as if 30 were added to t.
What is the value of t ?
(A) 4
(B)
(C) 5
(D)
(E) 10

10. Jeff plans to screenprint all 70 T-shirts in his print shop to complete an order.

He discovers that ten of the T-shirts he has in stock are the wrong size for this
order, and one-third of the T-shirts he can print do not print correctly. How
many correctly printed T-shirts does Jeff have for this order?
(A) 40
(B) 42
(C) 50
(D) 56
(E) 60

11. The 17 members of a crafting club are choosing a meeting night, with the

availability of all members represented in the rectangular region of the figure
above. Circular region W represents all members that can meet on

Wednesdays, and circular region T represents all the members that can meet
on Thursdays. If the numbers indicate how many people are in each of the

separate categories, how many people in the club cannot meet on Thursday?
(A)

5

(B)

7

(C)

8

(D) 11
(E) 12

Note: Figure not drawn to scale.
12. A portion of the graph of the function h is shown in the figure above. For how
many values of x shown in this portion does h(x) = 0 ?
(A) Four
(B) Three
(C) Two
(D) One
(E) Zero

13. In the rectangle above, point Z is located so that ZV + TV = ZU + TU. If SV
= 15 and TV = 39, what does ZV equal?
(A) 3
(B) 4
(C) 5
(D) 6
(E) 7

14. The chart above indicates the brands of pushpins available at a certain office

supply store. If Karen needs 100 pushpins to decorate her new bulletin board,
what is the least amount she could spend on enough pushpins at this store?
(A) $6.50
(B) $6.75
(C) $7.00
(D) $7.25
(E) $7.50

15. In the figure above, line segment

has a slope of − . What is the value of a

?
(A) 2.5
(B) 3
(C) 3.5
(D) 4
(E) 4.5

16. On a number line, the distance from the point that has coordinate k to the

16. On a number line, the distance from the point that has coordinate k to the

point with coordinate 3 is equal to 7 units. Which of the following equations
gives all possible values for k ?
(A) |k − 10| = 0
(B) |k − 7| = 3
(C) |k + 7| = 3
(D) |k − 3| = 7
(E) |k + 3| = 7

17. The sum of all odd integers from 1 to 303, inclusive, is 23,104. What is the
sum of all odd integers from 3 to 301, inclusive?
(A) 22,496
(B) 22,794
(C) 22,800
(D) 23,103
(E) 23,408

18. All values of c in which of the following intervals satisfy the inequality
<0?
I. −

<c−

II. − < c −
III. − < c −
(A) I only
(B) II only
(C) III only
(D) I and II
(E) II and III

19. In the equation fg = 81, where f and g are positive integers, how many
different values of f are possible?
(A) Two
(B) Three
(C) Four
(D) Five
(E) More than five

20. In the xy-coordinate plane, the vertices of ΔMNO are point M (r, s), point N

20. In the xy-coordinate plane, the vertices of ΔMNO are point M (r, s), point N

(3r, 0), and the origin O. If r and s are positive numbers, what is the area of
ΔMNO, in terms of r and s ?
(A)

rs

(B) rs
(C)

rs

(D)

r3s

(E) r3s

ST OP
If you finish before time is called, you may check your work on
this section only.
Do not turn to any other section in the test.

SECTION 3
Time — 25 minutes
24 Questions
(25-48)
Directions: For each question in this section, select the best answer from among the
choices given and fill in the corresponding circle on the answer sheet.

Each sentence below has one or two blanks, each blank indicating that something has
been omitted. Beneath the sentence are five words or sets of words labeled A through
E. Choose the word or set of words that, when inserted in the sentence, best fits the
meaning of the sentence as a whole.
Example:

Hoping to ------- the dispute, negotiators proposed a compromise that they felt would
be ------- to both labor and management.
(A) enforce . . useful
(B) end . . divisive
(C) overcome . . unattractive
(D) extend . . satisfactory
(E) resolve . . acceptable

25. Stephen’s new road bike was much more -------, even lighter, while his previous

25. Stephen’s new road bike was much more -------, even lighter, while his previous
one was a ------- form of transportation.
(A) diminutive . . speedy
(B) compact . . bulky
(C) commonplace . . competent
(D) gargantuan . . immense
(E) durable . . mechanical
26. Since the supermarket would no longer ------- its deli meats properly,

customers found it increasingly ——– to distinguish a strip steak from a pot
roast.

(A) clean . . redundant
(B) label . . forthright
(C) display . . delectable
(D) tag . . complicated
(E) restock . . arduous
27. The folk singer wrote songs that showcased the human spirit in all its forms,

always choosing to ——– the triumphant moments of one’s life, as well as the
sorrowful.

(A) undermine (B) articulate (C) personify (D) contradict
(E) underscore

28. The author’s new work was considered by many critics to be a(n) ------- novel,

28. The author’s new work was considered by many critics to be a(n) ------- novel,

since it used many elements and details that would have been out of place for
this story’s -------.

(A) anachronistic . . setting
(B) satirical . . medium
(C) subordinate . . rectitude
(D) archaic . . whimsy
(E) allegorical . . milieu
29. Reinhold was always backing down from his own arguments and deferring his

point of view to that of others; he therefore was consistently known for his ------.

(A) autonomy (B) brevity (C) erudition (D) tenacity (E) acquiescence

The passages below are followed by questions based on their content; questions

following a pair of related passages may also be based on the relationship between the

paired passages. Answer the questions on the basis of what is stated or implied in the
passage and in any introductory material that may be provided.
Questions 30-33 are based on the following passages.

30. Both passages primarily focus on

30. Both passages primarily focus on
(A) certain sports that are of interest to all fans
(B) particular hobbies that may be unhealthy
(C) some disdain from others for certain obsessions
(D) the elation felt by sports fans for talking about their interests
(E) the contempt sports fanatics feel towards those who know less than
them

31. The “family” in passage 1, line 6 would probably view the “sports fanatics” of
Passage 2, line 15 with

(A) marked agreement
(B) formal disgust
(C) sheer enthusiasm
(D) respectful consideration
(E) general disinterest
32. In line 4, “garnered” most nearly means
(A) given
(B) persuaded
(C) supplemented
(D) squandered
(E) displayed

33. Both passages make use of

33. Both passages make use of
(A) metaphor
(B) comparison
(C) personal experience
(D) hypothetical situations
(E) specific details
Questions 34-42 are based on the following passages.
This passage, adapted from a short story, presents an 11-year-old girl, Sarah, her father,
and her brother.

34. In lines 1-3, the phrases “an awful lot” and “all of a sudden” help to emphasize
Sarah’s

(A) disapproval of her father’s new girlfriend
(B) apathy toward her personal space being invaded
(C) wish that things could be as they once were
(D) unwillingness to accept a new person into her life
(E) surprise at a new development in her father’s home
35. In line 5, “basically” suggests that
(A) Sarah’s father bought his girlfriend a new house
(B) Sarah and her brother now live in the same room
(C) the house does not have all modern amenities
(D) Sarah invited Tess to live at the house
(E) Tess comes to the house very frequently

36. In context, “shifting around some furniture” (line 6) is best characterized as an
example of

(A) one of many possible improvements that a homeowner can make
(B) something typically done by someone who lives in the house containing
the furniture

(C) one of Sarah’s biggest problems with her father’s new girlfriend
(D) an aspect of home decorating in which Sarah is particularly interested
(E) the reason Tess is invited so often to the house
37. In lines 17-21, the author uses quotation marks to emphasize
(A) an insult that Tess’s family uses when referring to Sarah
(B) a joke between Sarah and her younger brother
(C) a slangy way of referring to family members
(D) a change in how people are referring to themselves
(E) a metaphorical way of describing a father’s love
38. In line 26, “Bride?” primarily serves to suggest that Sarah
(A) cannot hear Tess over the noisy car
(B) is unaware of a planned future event
(C) is acting like she does not know any words
(D) resists the idea of having Tess as a mother
(E) refuses to pay attention when Tess talks to her

39. The questions in lines 43-45 (“How … play?”) primarily serve to

39. The questions in lines 43-45 (“How … play?”) primarily serve to
(A) set up the scene in the next paragraph
(B) name specific topics of discussion
(C) demonstrate the depths of the disagreement
(D) suggest Sarah’s continued exclusion
(E) create suspense in a reader who wants to know the answers
40. In line 47, the phrase “barking orders” is primarily used to suggest
(A) an organized plan
(B) a calm attitude
(C) a pet-like docility
(D) an aggressive approach
(E) an open discussion
41. In line 63, her father’s question to Sarah suggests that he
(A) wishes Sarah would not invade his private moments with Tess
(B) resists the idea of getting married for a second time
(C) is aware that she is listening to the adult conversation
(D) will ask Sarah’s brother to be one of his groomsmen
(E) wants Sarah to forget about her mother altogether

42. The passage as a whole suggests that Sarah wishes that, in her family’s life, she

42. The passage as a whole suggests that Sarah wishes that, in her family’s life, she
were

(A) somewhere else
(B) away at school
(C) more involved
(D) getting married
(E) her brother’s age
Questions 43-48 are based on the following passages.
Online education refers to courses that are not taken in a traditional classroom but via
the Internet, with teachers and students working on computers. Both of the following
passages were published in 2014.

43. The first sentence of Passage 1 implies that online education
(A) is overly inexpensive
(B) is fashionable but ineffective
(C) has both good and bad aspects
(D) is declining in popularity
(E) has replaced traditional education

44. The sentence in lines 11-15 (“When … students”) serves primarily to

44. The sentence in lines 11-15 (“When … students”) serves primarily to
(A) mock the speech of administrators
(B) set up the anecdote that follows
(C) expand the idea in an earlier sentence
(D) provide incentives to buy a product
(E) express concern over a trend
45. Like the author of Passage 1, the author of Passage 2 most likely thinks of faceto-face education as

(A) collaborative and able to incorporate many media
(B) the last hope for aspiring professionals
(C) an outmoded way of relaying information
(D) exclusive to those who can afford it
(E) susceptible to compromising influences
46. As it is used in line 49, “diluted” most nearly means
(A) split
(B) flooded
(C) moistened
(D) purer
(E) weakened

47. The author of Passage 1 would most likely view the point made in lines 50-54,

47. The author of Passage 1 would most likely view the point made in lines 50-54,
Passage 2 (“The … courses”), as
(A) essentially correct
(B) bullishly wrongheaded
(C) exceedingly respectful
(D) subtly heavy-handed
(E) unreasonably cruel
48. Both passages cite the 77 percent statistic in order to make a point about
(A) widespread disapproval
(B) perceived effectiveness
(C) academic methodologies
(D) traditional models
(E) learning objectives

ST OP
If you finish before time is called, you may check your work on
this section only.
Do not turn to any other section in the test.

SECTION 4
Time — 25 minutes
18 Questions
(21-38)
Directions: For this section, solve each problem and decide which is the best of the
choices given. Fill in the corresponding circle on the answer sheet. You may use any
available space for scratchwork.

Notes
1. The use of a calculator is permitted.
2. All numbers used are real numbers.
3. Figures that accompany problems in this test are intended to provide information
useful in solving the problems. They are drawn as accurately as possible

EXCEPT when it is stated in a specific problem that the figure is not drawn to
scale. All figures lie in a plane unless other wise indicated.

4. Unless otherwise specified, the domain of any function f is assumed to be the set
of all real numbers x for which f(x) is a real number.

Reference Information

The number of degrees of arc in a circle is 360.
The sum of the measures in degrees of the angles of a triangle is 180.

t<6

t<6

16 < 4t
21. If t is an integer that satisfies the inequalities above, what is the value of t ?
(A) 2
(B) 3
(C) 4
(D) 5
(E) 6

22. In the figure above, ABCD is a square. If W is the midpoint of AB, X is the

midpoint of BC, and Y is the midpoint of CD, which of the following is NOT
equal to BC ?

(A) AD + AW
(B) AW + XC
(C) CD
(D) DY + BW
(E) AD + CY – AW

6 + 4z = 20

6 + 4z = 20
23. How many values for z satisfy the equation above?
(A) Zero
(B) One
(C) Two
(D) Three
(E) More than three

24. If 10 < s3 < 12 and
(A) 2
(B) 4
(C) 5
(D) 8
(E) 20

= s, which of the following could be the value of t ?

25. In the figure shown above, the large rectangular solid has been divided into 6

congruent cubes. If the face of each cube has an area of 3 square inches, what
is the total surface area of the rectangular solid, in square inches?
(A) 22
(B) 33
(C) 50
(D) 66
(E) 132

26. If

is negative and x < 0, which of the following is negative?
(A) x3
(B) y2
(C) –y
(D) 2x
(E) y

Note: Figure not drawn to scale.
27. The sectors of the circular dart board shown in the figure above are each
painted one of three colors: blue, green, or red. The probability that a thrown
dart that hits the dart board will land in a red sector is

. If the central angle

of each red sector has degree measure r, what is the value of r ?
(A) 30
(B) 45
(C) 55
(D) 60
(E) 90

28. Several values of the functions g and h are shown in the table above. For which
of the following values of x is g(x) = h(1) ?
(A) 0
(B) 1
(C) 2
(D) 3
(E) 4

29. For each pair (x, y) in the table above, x = , where k is a constant. What is
the value of k ?

30. For each chore Kevin completes, his mother gives him 8 dollars. If Kevin’s

mother gave him less than 1,500 dollars for doing chores last month, what is
the greatest possible number of chores Kevin could have completed last
month?

31. In the figure above, a || b and c || d. What is the value of x ?

What will you do during your summer vacation?

What will you do during your summer vacation?

32. In a survey, 600 high school juniors each selected one of six responses to the
question “What will you do during your summer vacation?” The results are
shown in the circle graph above. How many of the high school juniors
selected a response other than “Go to the beach?”

33. If the area of circle P is 121π, what is the diameter of circle P ?

If 12 and 9 are factors of z,

then 12 × 9 is a factor of z.
34. If z is a positive integer less than 120, what is one possible value of z that
proves the statement above false?

35. The figure above shows three small right triangles inside one large right

triangle. If the area of triangle A is 18, the area of triangle B is 8, and the area
of triangle C is 2, what is the area of the shaded region?

36. If

=

and

=

, then

=

37. How many integers between 100 and 1,000 have at least one digit that is a
four?

38. Ben and Carl left school at the same time and each drove directly to his own
house. Ben drove an average speed of 20 miles an hour, and Carl drove an

average speed of 15 miles per hour. Ben and Carl arrived at their respective

houses at the same time. If Ben drove 15 miles further than Carl did, how far,
in miles, did Ben drive?

ST OP

If you finish before time is called, you may check your work on
this section only.
Do not turn to any other section in the test.

SECTION 5
Time — 30 minutes
30 Questions
(1-39)
Directions: For each question in this section, select the best answer from among the
choices given and fill in the corresponding circle on the answer sheet.

The following sentences test correctness and effectiveness of expression. Part of each

sentence or the entire sentence is underlined; beneath each sentence are five ways of
phrasing the underlined material. Choice A repeats the original phrasing; the other

four choices are different. If you think the original phrasing produces a better sentence
than any of the alternatives, select choice A; if not, select one of the other choices.

In making your selection, follow the requirements of standard written English; that is,

pay attention to grammar, choice of words, sentence construction, and punctuation.
Your selection should result in the most effective sentence—clear and precise, without
awkwardness or ambiguity.
EXAMPLE:
Bobby Flay baked his first cake and he was thirteen years old then.
(A) and he was thirteen years old then
(B) when he was thirteen
(C) at age thirteen years old
(D) upon the reaching of thirteen years
(E) at the time when he was thirteen

1. The Great Wall of China, which was built to protect the Chinese Empire from

1. The Great Wall of China, which was built to protect the Chinese Empire from
invasion, and it extends over more than 13,000 miles.

(A) which was built to protect the Chinese Empire from invasion, and it
extends

(B) was built to protect the Chinese Empire from invasion, it extends
(C) built to protect the Chinese Empire from invasion, therefore extending
(D) which was built to protect the Chinese Empire from invasion, extends
(E) it was built to protect the Chinese Empire from invasion, extending
2. Every winter, hundreds of drivers ignoring official warnings to remain at home
while heavy snow is falling, only to crash into other vehicles and cause major
accidents on the highway.
(A) drivers ignoring
(B) drivers ignore
(C) drivers in their ignoring
(D) drivers who ignore
(E) drivers, when ignoring

3. Walking the moon’s surface for slightly more than two hours, numerous photos

3. Walking the moon’s surface for slightly more than two hours, numerous photos
were taken by Neil Armstrong and Buzz Aldrin of Little West Crater.

(A) numerous photos were taken by Neil Armstrong and Buzz Aldrin of
Little West Crater

(B) numerous photos of Little West Crater were taken by Neil Armstrong
and Buzz Aldrin

(C) photos of Little West Crater, many of them were taken by Neil
Armstrong and Buzz Aldrin

(D) Neil Armstrong and Buzz Aldrin took, of Little West Crater, numerous
photos

(E) Neil Armstrong and Buzz Aldrin took numerous photos of Little West
Crater

4. Chiropractic methods of treatment, once commonly criticized by many in the
medical field, appear to be gaining general acceptance among health care
professionals.

(A) appear to be gaining
(B) although gaining
(C) but they appear to have gained
(D) will appear to have gained
(E) but gaining

5. The largest and most diverse rainforests in the world is found in the South

5. The largest and most diverse rainforests in the world is found in the South

American Amazon Basin, which includes regions belonging to nine different
nations.

(A) is
(B) that are
(C) are
(D) having been
(E) were
6. After the Curies discovered radium in 1898, this element became known for its
damaging effects upon humans, some are mutated cells, ulcers, and cancer.
(A) some are
(B) those effects include
(C) they are
(D) such as
(E) among them was
7. Though most famous for her relationship with Beatles singer John Lennon, the

important contributions of Yoko Ono include her work in art, peace, and AIDS
outreach programs.

(A) the important contributions of Yoko Ono include her work in
(B) Yoko Ono has been an important contributor to
(C) Yoko Ono’s important contributions include her work in
(D) the important contributions of Yoko Ono would have been her work in
(E) the works of Yoko Ono are important contributions to

8. Genghis Khan united many nomadic tribes of northeast Asia in the early

8. Genghis Khan united many nomadic tribes of northeast Asia in the early
thirteenth century and founded the Mongol Empire.
(A) century and founded
(B) century, who founded
(C) century and to found
(D) century, he also founded
(E) century and founding
9. When a teacher cares about her classes, she prepares for them carefully, and
often late at night, which demonstrated that they were important to her.

(A) them carefully, and often late at night, which demonstrated that they
were important

(B) it carefully, often late at night, and this demonstrates that it is
important

(C) it carefully, often late at night, so it demonstrates that it is important
(D) them carefully, often late at night, which demonstrates that it is
important

(E) for them carefully, often late at night, thereby demonstrating that they
are important

10. Rebekah chose a wedding date, discovered that it was a date that most of her
invited guests could not attend, and it was postponed until the following
Saturday.

(A) and it was postponed
(B) she then postponed it
(C) postponing it
(D) then postpone it
(E) and then postponed it
11. Ludovic built a house of cards that was enormous but simultaneously it was

11. Ludovic built a house of cards that was enormous but simultaneously it was
very fragile as well.

(A) a house of cards that was enormous but simultaneously it was very
fragile as well

(B) an enormous house of cards, it was simultaneously very fragile
(C) a house of cards that was enormous and as well simultaneously very
fragile

(D) an enormous but very fragile house of cards
(E) an enormous and simultaneously very fragile house of cards
12. As the autumn wore on, the temperatures start to drop below freezing on a
regular basis.

(A) start to drop
(B) started to drop
(C) start dropping
(D) have started dropping
(E) are beginning to drop

13. Walkway Over the Hudson, originally a railroad bridge and part of the

13. Walkway Over the Hudson, originally a railroad bridge and part of the

Poughkeepsie Bridge Route, now used by locals as a pedestrian walkway.
(A) part of the Poughkeepsie Bridge Route, now used by locals as a
pedestrian walkway

(B) part of the Poughkeepsie Bridge Route, which is now used by locals as a
pedestrian walkway

(C) part of the Poughkeepsie Bridge Route, is now used by locals as a
pedestrian walkway.

(D) It was part of the Poughkeepsie Bridge Route, being used today by
locals as a pedestrian walkway

(E) used today by locals as a pedestrian walkway, and it was once part of
the Poughkeepsie Bridge Route

14. The gecko’s feet are different than other lizards such as the iguana or the
Komodo dragon.

(A) different than other lizards
(B) different than those of other lizards
(C) different than other lizards’ feet
(D) unlike seeing other lizards
(E) unlike other lizards
15. The biologist observed the similarities between the results of his own

experiments with what resulted from Watson and Crick’s experiments more
than sixty years previously.

(A) with what resulted from Watson and Crick’s
(B) with Watson and Crick’s
(C) and also Watson and Crick’s
(D) and those of Watson and Crick’s
(E) and Watson and Crick’s

16. By planning to arrive early to the concert is why Carl was confident that he
would be able to find a seat right in front of the stage.

(A) By planning to arrive early to the concert is why
(B) His planning to arrive early to the concert ended in that
(C) Due to his plan of arriving early to the concert,
(D) Because he planned to arrive early to the concert,
(E) He planned to arrive early to the concert is the reason
17. Nikola Tesla was a remarkable scientist not only because he made numerous
contributions towards the fields of x-ray imaging and radio but he patented
more than 300 inventions.

(A) radio but he patented
(B) radio, he also patented
(C) radio, but also because he patented
(D) radio but because he patented also
(E) radio but he also patented
18. Alzheimer’s disease causes memory loss and confusion; for instance, those
affected frequently forget the names of close friends and relatives.
(A) confusion; for instance, those affected frequently forget
(B) confusion, forgetting, as for instance,
(C) confusion; for instance, often forgetting
(D) confusion, a for instance is when they forget
(E) confusion, often forgetting, for instance

19. In 1505, Michelangelo started building Pope Julius II’s tomb but never

19. In 1505, Michelangelo started building Pope Julius II’s tomb but never

finishing it to his satisfaction, perhaps because he was constantly distracted by
other tasks.

(A) tomb but never finishing it to his satisfaction, perhaps because he was
constantly distracted by other tasks

(B) tomb, however, it was never finished to his satisfaction, perhaps
because he was constantly distracted by other tasks

(C) tomb, although distracted, perhaps, by other tasks, it was never
completed to his satisfaction

(D) tomb, he never finished it to his satisfaction however, perhaps because
he was constantly distracted by other tasks

(E) tomb, but, perhaps because he was distracted by other tasks, he never
completed the tomb to his satisfaction

20. The claims made by the witnesses, particularly the statements of the victim,

has convinced the jury that the defendant is guilty and returned a verdict of
guilty.

(A) has convinced the jury that the defendant is guilty and returned
(B) have convinced the jury to return
(C) has created so much conviction among the jury that it has returned
(D) have convinced the jury, returning
(E) have so convinced the jury that they have returned
The following sentences test your ability to recognize grammar and usage errors. Each

sentence contains either a single error or no error at all. No sentence contains more
than one error. The error, if there is one, is underlined and lettered. If the sentence
contains an error, select the one underlined part that must be changed to make the

sentence correct. If the sentence is correct, select choice E. In choosing answers, follow
the requirements of standard written English.
EXAMPLE:

21.

22.

23.

24.

24.

25.

26.

27.

27.

28.

29.

30.

31.

32.

32.

33.

34.

Directions: The following passage is an early draft of an essay. Some parts of the
passage need to be rewritten.

Read the passage and select the best answers for the questions that follow. Some

questions are about particular sentences or parts of sentences and ask you to improve
sentence structure or word choice. Other questions ask you to consider organization

and development. In choosing answers, follow the requirements of standard written
English.

Questions 35-39 are based on the following passage.

Questions 35-39 are based on the following passage.
(1) Since prehistoric times, painters have been creating portraits of celebrities,

nobility, and other notable individuals.(2) The talents of some painters have

proven to be particularly well-suited to the task of portrait painting. (3) John

Singer Sargent, for example. (4) All of his portraits have been displayed in famous
museums such as the Metropolitan Museum of Art in New York City and the

National Gallery in London. (5) Of these, The Lady with the Rose is considered his
best loved and most widely exhibited work.

(6) The task of accurately capturing not just the photographic likeness, but also

the inner essence of the subject, is a challenging one. (7) In proper portrait

painting, the subject’s mouth should remain relatively neutral, not smiling openly
or frowning, so the artist must find ways to convey expression through the eyes

and eyebrows. (8) Faced with this difficulty, Paul Cézanne focused on capturing a
single moment in time, and would sometimes take hours to complete a single

brush stroke. (9) He frequently required as many as 150 sittings from his subjects,

spending hours on a single feature. (10) Doing this proved worthwhile: his Portrait
of Louis-Auguste Cézanne, Father of the Artist, reading ‘l'Evénement was displayed at
the prestigious Paris Salon.

(11) Subjects are often dissatisfied with their portraits, especially if they feel

that their best features have not been emphasized or if they do not feel as if the

painting does not convey the proper image of their persona. (12) When Sargent’s
Portrait of Madam X aroused scandal due to its subject’s pose and dress, the
reaction caused the sitter, Amélie Gautreau, to reject the painting. (13)

Nevertheless, when it comes to portrait painting, a flattering portrayal will not
ensure the subject’s approval. (14) As a portrayal of George Washington, John

Trumbull’s portrait General George Washington was rejected by the committee that
had commissioned it. (15) Trumbull was a respected painter whose Declaration of
Independence was used on the two-dollar bill.

35. What is the best version of the underlined portions of sentences 3 and 4

35. What is the best version of the underlined portions of sentences 3 and 4
(reproduced below)?

John Singer Sargent, for example. All of his portraits have been displayed in

famous museums such as the Metropolitan Museum of Art in New York City and
the National Gallery in London
(A) (No change)
(B) All of John Singer Sargent’s portraits, for example, have
(C) There is John Singer Sargent, for example. His portraits have all
(D) For example, John Singer painted many portraits, and all of them have
(E) John Singer Sargent, for example, whose portraits have all
36. Which of the following, if placed at the beginning of sentence 6 (reproduced
below), would provide the most effective transition between the first and
second paragraphs?

The task of accurately capturing not just the photographic likeness, but also the
inner essence of the subject, is a challenging one.

(A) Although portrait painters have been popular for centuries,
(B) Because of the focus on photographic accuracy,
(C) With such demand from subjects,
(D) But no matter how attractive a person is,
(E) It may require time to become a skilled painter, but

37. In context, which of the following is the best revision of the underlined section

37. In context, which of the following is the best revision of the underlined section
of sentence 10 (reproduced below)?

Doing this proved worthwhile: his Portrait of Louis-Auguste Cézanne, Father of
the Artist, Reading ‘l’Evénement was displayed at the prestigious Paris Salon.
(A) (No change)
(B) Painting Impressionist works
(C) His effort had
(D) That has eventually
(E) This meticulousness
38. Which of the following sentences would best be placed at the beginning of
paragraph 3, before sentence 11?

(A) Some portrait artists have become quite famous.
(B) We may not always realize how the length of time required to a paint
quality portrait.

(C) Most of us have seen portraits hanging in museums.
(D) Some portraits have not been so well received.
(E) There are a number of instances that show this to be true.
39. In context, which of the following is the best version of the first underlined
portion of sentence 14 (reproduced below)?

As a portrayal of George Washington, John Trumbullís portrait General George
Washington was rejected by the committee that had commissioned it.
(A) (No change)
(B) Following
(C) Even though it complimented
(D) With its presentation of
(E) Arguably an accurate portrayal

ST OP
If you finish before time is called, you may check your work on
this section only.
Do not turn to any other section in the test.

PRACTICE TEST 2 ANSWERS

You will find a detailed explanation for each question beginning on
this page.

SCORING YOUR PRACTICE PSAT
Critical Reading
After you have checked your answers against the answer key, you
can calculate your score. For the two Critical Reading sections
(Sections 1 and 3), add up the number of correct answers and the
number of incorrect answers. Enter these numbers on the worksheet
on the next page. Multiply the number of incorrect answers by .25
and subtract this result from the number of correct answers. Then
round this to the nearest whole number. This is your Critical
Reading “raw score.” Next, use the conversion table to convert your
raw score to a scaled score.

Math
Calculating your Math score is a bit trickier, because some of the
questions have five answer choices (for these, the incorrect answer
deduction is .25), and some are Grid-Ins (which have no deduction
for wrong answers).
First, check your answers to all of the problem-solving questions on
Sections 2 and 4. For Section 2 and questions 21–28 of Section 4,
enter the number of correct answers and the number of incorrect
answers into the worksheet on the next page. Multiply the number of
incorrect answers by .25 and subtract this result from the number of
correct answers. For questions 29–38 of Section 4, the Grid-In
questions, simply enter the number of correct answers. Now, add up
the totals for both types of math questions to give you your total
Math raw score. Then you can use the conversion table to find your
scaled score.

Writing Skills
The Writing Skills section should be scored just like the Critical
Reading sections. Add up the number of correct answers and the
number of incorrect answers from Section 5, and enter these
numbers on the worksheet on the next page. Multiply the number of
incorrect answers by .25 and subtract this result from the number of
correct answers. Then round this to the nearest whole number. This
is your Writing Skills raw score. Next, use the conversion table to
convert your raw scores to scaled scores.

WORKSHEET FOR CALCULATING YOUR
SCORE

SCORE CONVERSION TABLE

Chapter 8
Practice Test 2: Answers and
Explanations

Section 1
1. B Since the coach didn’t want the opposing team to pick up her
signals, she therefore wanted to keep them secret.
“Secretive” would be a good word to put in the blank.
Eliminate choice (A), which is a trap since this sentence
deals with sports. Choices (C), (D), and (E) do not match
“secretive,” so choice (B) is the best answer.
2. C Start with the first blank. The clues of spears, traps, and
cudgels are typically involved with hunting, so eliminate
everything except choices (C) and (D). Now work the
second blank. Since the sentence says that this activity was
necessary for the head of the household, the second blank
should be something like “symbol” or “prime example.”
Eliminate choice (D) since it doesn’t match. Choice (C) is
the correct answer.
3. D Start with the second blank. The sentence states that his
personal temperament has never been agreed upon, so you
know there is a disagreement about Ty Cobb. Since there
are clues stating he had instances of kindness and generosity,
find something for the second blank that is the opposite of
those traits. Eliminate everything but choices (A) and (D)
since irritability and irascibility are both opposites of the
clues. Since it’s clear that he has different temperaments, the
first blank should indicate that his bad behavior stands in
opposite of his good behavior. The first blank should be
something that means “goes against.” Eliminate choice (A)
since highlighted does not fit. Choice (D), overshadowed, is
the correct answer.
4. A Since the chef believed that originality was a far better attribute
of good cooking than mere skill, the first blank will need

something that mirrors originality and the second blank will
need to match skill. Start with the first blank and eliminate
everything but choices (A) and (C). Now work with the
second blank. Eliminate choice (C) because opulence means
“extravagance,” and is therefore incorrect. Choice (A) is the
correct answer.
5. C Since Raphael was always in contrast with what Ms. Banks
expected from her students, look for opposites of the clues.
Start with the first blank, which needs to be the opposite of
punctual. Eliminate everything except choices (B) and (C)
since sluggish means “slow” and could fit the blank. The
second blank needs to be the opposite of disrespectful. Both
dutiful (which means “obedient”) and deferential (which
means “respectful”) are possibilities, but the combination of
words in choice (C) is a better fit, so eliminate choice (B).
Choice (C) is the correct answer.
6. A The clue here is that the film looks only at the origins of the
story’s characters. Therefore, the blank should be something
that means “beginning.” Choice (A) fits the blank, since
prelude means “beginning.” Picaresque means “humorous
adventure,” so eliminate choice (B). A Roman a clef is
“historical fiction,” so eliminate choice (C). An anachronism
is something that is “out of place” while an epilogue is the
opposite of beginning, so get rid of both choices (D) and
(E). Choice (A) is the correct answer.
7. E Since the sentence contrasts the films of the 1980s, which
were considered clichéd and commercial, with those of the
1970s, the words for the two blanks will be the opposites of
each other. The first blank should be the opposite of clichéd,
so look for something that means “not clichéd” or
“original.” Eliminate everything but choices (B) and (E).
The second blank needs to be the opposite of commercial, so
look for something that means “not intended for a mass

market.” Eliminate choice (B) since ubiquitous means
“abundant.” Choice (E) is the correct answer.
8. A The clue here is that the auto mechanic can figure out a
problem prior to inspection, so therefore we need a word in
the blank that means “having foresight or being able to see
in the future.” Choice (A) matches these words well.
Scintillating is sometimes used to describe intelligence, but it
means “shining brightly,” so eliminate choice (D). Choice
(B) means “working well,” so eliminate it. Choice (C) means
to “experience through watching others,” and choice (E)
describes children with “advanced abilities beyond their
age,” so eliminate them. Choice (A) is the correct answer.
9. C The main idea in this passage is that Samuel’s limited
English skills were actually good for him in his current job,
since he didn’t question some of the odd phrases used in the
kitchen. Therefore, the author uses those phrases in order to
portray Samuel’s limited English as helpful. Eliminate
choice (A), since this is not mentioned. Choice (B) seems
like it could work, but the author is not placing any
emphasis on whether or not the phrases are silly. Choice (C)
seems to match the prediction, so keep it. Choices (D) and
(E) are not mentioned, so eliminate them. Choice (C) is the
correct answer.
10. A Since it’s stated that Samuel’s lack of English skills actually
helped him in his current job, the correct answer will be
something that means “helpful.” Choice (A) fits, so keep it.
Choice (B) is negative, so eliminate it. Choice (C) is a
positive word, but the passage never mentions whether
Samuel likes his job, so eliminate it. Choice (D) doesn’t
mean “helpful,” while choice (E) is a trap answer since it’s
associated with food, so eliminate both answers. Choice (A)
is the correct answer.

11. B The author states at the beginning of the passage that sugar,
once considered a common ingredient of sweet foods such
as candies, has also become common in more unexpected
foods, such as breads and salad dressings. So the correct
answer should show how sugar is part of such a wide range
of foods. Choice (A) is only half right, since bread is not
commonly associated with sugar. Choice (B) is a good
match, so keep it. Choice (C) doesn’t work since the author
isn’t expressing caution and choice (E) doesn’t work since
the author doesn’t criticize the use of sugar. Choice (D),
while it may seem to fit the author’s main idea, is too
extreme. Choice (B) is the correct answer.
12. E The question states that the author suggests something
about sugar, so find an answer that is definitely true based
on the passage. Choice (A) is incorrect since the passage
never states that sugar or narcotics are the most addictive
substances. Choice (B) doesn’t work since the passage never
states that the humans and rats process foods in the same
way and choice (D) can be eliminated since most is too
extreme. Choice (C) seems okay, except the passage only
states that sugar has become more widespread over the past
several decades, so there is no evidence to suggest that
there is more now than exactly 10 years ago. Choice (E),
the correct answer, is true because it is stated in the last
sentence.
13. C The word “overflowing” suggests that there have been many
Western projects to modernize the Middle East. This is a fairly
general statement, so the specifics in choices (A) and (B)
cannot be supported. Choices (D) and (E) do not address
these Western projects at all, so they too can be eliminated.
14. A The sentence in which Bill Clinton appears reads as follows:
President Bill Clinton, for example, is still praised for his role in
Israeli-Palestinian talks, and a few sentences later, the author

goes on to say, This attitude toward non-Western regions, the
belief that the West’s systems of government can help save the
people of the Middle East.… Therefore, it can be inferred that
Bill Clinton is a representative of this attitude, as choice (A)
suggests. The author goes on to criticize this attitude, so
choices (B), (D), and (E) can be eliminated. Choice (C) can
also be eliminated because Clinton is the only example
given.
15. D Another way of saying universally applicable would be
“appropriate to all.” The author is stating in these lines that
Western styles of government may not be appropriate for all
people, especially those outside the West, as choice (D)
indicates. The author goes on to suggest a need for more
non-Western perspectives, therefore eliminating choices (A),
(B), and (E). Choice (C) is too extreme in its use of the word
only, so it can be eliminated. Choice (D) remains as the
correct answer.
16. D The relevant lines state the following: The native peoples who
are then forced to live under the new government’s rule become
extremely skeptical of it, as its supposed successes are measured
by seemingly irrelevant metrics. The key words here are
extremely skeptical, which agree most closely with choice (D)
and disagrees with choice (E). The information in the
passage is not specific enough to support choices (B) or (C).
Choice (A) is too extreme in its use of the word despise, so it
can be eliminated.
17. C The relevant lines state the following: Many of the great
ancient and historical societies come from these regions, but
since the seventeenth century, these regions have been
considered almost universally backward. In other words, these
regions were once considered “great” but are now
considered “backward,” as choice (C) suggests. These lines
do not address contemporary governments, which

eliminates all other choices.
18. B This paragraph discusses the influence of George Bush and
others, suggesting that this influence has not been a good
one, as choice (B) suggests. The lines do not contain specific
support for the other choices, so (A), (C), (D), and (E) can
be eliminated.
19. E Cross out the word in the context and replace it with your
own: For many Westerners, nationality is a given and
ultimately ______ the more local identifications of town, city, or
state. A word like supersedes or replaces would work here, in
which case only choice (E) comes close. The other choices
may represent other meanings for the word trumps, but they
do not work in this context.
20. A Cross out the word in the context and replace it with your
own: The Western notions of nation-above-all and religious
coexistence can’t ________ in this and other countries because the
value systems have developed so independently of these notions.
Some word like apply or function would work here, in which
case only choice (A) comes close. The other choices may
represent other meanings for the word maintain, but they do
not work in this context.
21. B This question asks for a statement that would refute the
author’s claim in the lines, As in many other parts of the
world, “Iraqi freedom” was defined by someone other than the
Iraqis themselves. Any statement that would suggest that
Iraqis or some other group had a role in defining their own
government systems would refute this claim, so choice (B)
provides the best refutation. Choices (A), (C), (D), and (E)
all support the author’s central claim that the West has had
a too-powerful influence in the region.
22. D The author writes for the most part about the negative

effects of Western influence in the Middle East, but the
lines, Certainly, Western nations are today more sensitive to
cultural differences than they have ever been, suggest that this
influence may be improving. Choice (D) reflects this
concession and slight change of tone. It does not reflect the
author’s broader point, however, which eliminates choices
(A), (B), (C), and (E).
23. C The relevant sentence says the following: It still remains to be
seen, however, whether this new multicultural stance is a
genuine change or a simple repackaging of an old product. In
this case, the simple repackaging is contrasted with a genuine
change. The author is therefore skeptical that this new
approach is a genuine change, as suggested in choice (C).
The author does not hope for this simple repackaging,
eliminating choice (A), (B), and (E). Choice (D) takes the
word product too literally.
24. D The author argues throughout the passage that the influence
of the West has been too strong in the Middle East and that
there needs to be more local influence in government
policy. Choice (D) best reflects this main idea. Choices (A),
(C), and (E) go against this goal. Choice (B) is also an
example of a Western ideal, so it too can be eliminated.

Section 2
1. D Given variables in the answer choices, Plug In. If x = 2
ounces of cinnamon, at $3 per ounce, the cost would be $6.
This is the target answer, so check the answer choices to see
which one equals 6. Choices (A) and (E) can be eliminated,
since those numbers are not 6. Choice (B) equals , which
does not equal 6 and can be eliminated. Choice (C) equals
, which does not equal 6 and can be eliminated. Choice (D)
is 3(2), which does equal 6. Choice (D) is the credited
response.
2. A When asked for the value of a variable, Plug In the Answers
(PITA). Start with choice (C), and plug in 1 for h. The
equation becomes 5.73 × 101 = 5.73 × 10 = 57.3. This is
too big, so eliminate (C). Choices (D) and (E) will also be
too big, so eliminate those as well. For choice (A), the
equation is 5.73 × 10–2 = 5.73 × 0.01 = 0.0573.
Therefore choice (A) is the credited response.
3. C This seems like a Plugging In problem, because of the
variables, or like one in which solving for a and b would
help. However, the question asks for a value in terms of 3a
and 2b, quantities which are already given. Therefore, 2(3a)
+ 4(2b) becomes 2(5) + 4(9) = 10 + 36 = 46. Choice (C)
is the credited response.

4. B To solve average questions, draw an average pie. The total
goes in the top space. In this problem, though the
individual numbers are unknown, the total for a + b + c +
d + e equals the sum of a and b plus the sum of c, d, and e.
Therefore, Total = 18 + 37 = 55. Place this number in the
top space and the number of things, which is 5, in the lower
left space.

The average is the total divided by the number of things. In
this case, that is 55 ÷ 5 = 11, so (B) is the credited
response.
5. E If triangle LMQ is an equilateral triangle and LM = 2, then
MQ = 2 as well. For this same reason, if MN = 3, then MO
= 3 as well. Opposite sides of a parallelogram are equal, so
side OP of MOPQ is equal to 2 and side PQ is equal to 3.
Therefore, the perimeter of parallelogram MOPQ is 3 + 2
+ 3 + 2 = 10, and (E) is the credited response.
6. B When the question asks for a specific value and there are
numbers in the answers, Plug In the Answers. Start with
choice (C), and plug in
for the expression (x + y) in
the equation. This gives us 13 – (
)2 = 4, which is 13 –
17 = –4. Choice (C) is wrong, so let’s try choice (B) and
plug in –3 for the expression (x + y). 13 – (–3)2 = 4, which
translates to 13 – 9 = 4. Since this is true, (B) is the
credited response.

7. D The question does not indicate that the figure is “not drawn
to scale,” so start by ballparking. The angle with
measurement z° is obtuse, so (A) and (B) can be eliminated.
Since quadrilateral FJKL is the reflection of quadrilateral
FGHJ, ∠JFL will have the same measurement as ∠GFJ,
which is 40°. Line y is a straight line, so the measurement of
∠JFL plus z° equals 180°. Therefore, z = 140, so (D) is the
credited response. The information that ∠FJK equals 120° is
a distraction and is not necessary to solve this problem.
8. A If 50 + p = 180, then p = 130°. Therefore, ∠p is obtuse,
so the acute angles in (C), (D), and (E) can be eliminated.
Of the two remaining angles, (B) appears to be just greater
than 90°, whereas (A) looks to be in between 90˚ and 180˚.
Choice (A) is closer is 130°, so (A) is the credited response.
9. E When asked for a specific value and given numbers in the
answer choices, PITA. Start with (C) and assume that t = 5.
When 5 is quadrupled, or multiplied by 4, the result is 20.
When 30 is added to 5, the result is 35. These results are
not the same, so (C) can be eliminated. A greater number
than 5 is needed to bring the two results closer together;
eliminate choices (A) and (B). Choice (D) contains a
fraction that is more difficult to plug in, so try (E). When 10
is quadrupled, the result is 40. When 30 is added to 10, the
result is also 40, so (E) is the credited response.
10. A If Jeff has 70 shirts total but 10 are the wrong size, he only
has 60 shirts that he can print for this order. One-third of
those 60 shirts, or 20 of them, do not print correctly. This
leaves 40 shirts that are correctly printed, making (A) the
credited response.
11. E There are 17 total members in this crafting club. All of them
can either meet on Thursday or they cannot meet on
Thursday. To find how many of them cannot meet on

Thursday, add up every member outside the Thursday
region. This includes the 4 members who cannot meet
either Wednesday or Thursday and the 8 members who can
only meet Wednesday but not Thursday. 4 + 8 = 12
members who cannot meet on Thursday.
Alternatively, the same result can be achieved by
subtracting the number that can meet on Thursday from the
total number of members. In this case, the number of
members that can meet on Thursday include the 2 who can
also meet on Wednesday plus the 3 who can only meet on
Thursday, or 5 of the members. Subtract these 5 from the
total 17 to get 12 who cannot meet on Thursday.
Either way, the result is 12, and (E) is the credited response.
12. B When dealing with graphs of functions, f(x) or h(x) is the y
value for any given x. The question asks how many values
of x make h(x) = 0, so draw a line on the graph at y = 0.
This is also the x-axis of the xy-coordinate plane. The
number of points of intersection between the graph of h(x)
and the line drawn will be the number of values for which x
makes h(x) = 0.

There are three points of intersection, so (B) is the credited
response.
13. D When asked for a specific value, PITA. First, though, the
figure needs to be labeled and the lengths of all sides
determined. Start by labeling the given lengths on the
figure. Since it is a rectangle, opposite sides are equal, so
label those as well. Also, find the length of UV, either by
using the Pythagorean Theorem or the fact that these
triangles are the 5:12:13 Pythagorean triple with each side
multiplied by 3. Therefore, UV equals 36.

With the figure labeled, it is time to PITA. Start with (C),
and plug in 5 for ZV. If ZV = 5, then ZU = 31, since UV =
36. Now check if ZV + TV = ZU + TU by plugging in the
values for each segment. This becomes 5 + 39 = 31 + 15
or 44 = 46. This is not true, so (C) is not the correct value
and can be eliminated. A larger number is needed for ZV to
make the left side of the equation larger, so eliminate (A)
and (B) as well. For (D), ZV = 6 and ZU = 30. ZV + TV =
ZU + TU becomes 6 + 39 = 30 + 15 or 45 = 45. This is
true, so (D) is the credited response.

14. A From the chart, it is difficult to determine which brand of
pushpins is the cheapest per pin. For each brand, take the
cost and divide by the number of pins to get the cost per
pin. For Bob’s, this is
this is

= $0.075 per pin. For Pokey’s,

= $0.0625 per pin. For Thumbelina’s, this is

= $0.0595 per pin. Thumbelina’s are the lowest price
per pin and the best value, so Karen should start with those.
If she buys 2 packages of Thumbelina’s at $2.50 each, she
will spend $5.00 for 84 pushpins. She needs 100 pushpins
total, so she still needs 16. To spend the least amount of
money, she should get one package of Bob’s, since those
have at least as many as she needs at the lowest cost. This
adds another $1.50 to her total spending, bringing it to
$6.50. Choice (A) is the credited response.
15. D When asked for a specific value and given numbers in the

answer choices, PITA. Starting with (C), plug the value for a
into the slope formula:

or

. For (C), the slope is

. This is not equal to − , so (C) can be
eliminated. The value in (C) yielded a slope that was too
small, so a bigger value of a is needed. Therefore, (A) and
(B) can also be eliminated. For (D), the slope is
, so (D) is the credited response.
16. D The question describes a number line, so draw one to make
the numbers easier to visualize. Mark the point with
coordinate 3 and then the two points that sit at a distance
of 7 from that point.

Therefore, the two numbers at a distance of 7 from the
point 3 are –4 and 10. Plug these numbers for k into the
expressions in the answer choices to determine which one is
true. Choice (A) is |−4 −10 = 0, or |−14|= 0. This is not
true, so (A) can be eliminated without checking if 10 will
make the equation true.
Choice (B) is |−4 − 7| = 3, or |−11| = 3. This is not
true, so (B) can also be eliminated. Choice (C) is |− + 7|
= 3, or |3| = 3. This is true, so check if 10 makes the
equation true. |10 + 7| = |17|, which is not equal to 3, so
(C) can be eliminated. Choice (D) is |−4 − 3|= 7, or |−7|
= 7. This is true, so check if 10 makes the equation true.

|10 − 3| = 7, or |7| = 7. This is also true, so (D) is the
credited response.
17. C The question gives the sum of the odd integers from 1 to
303, and then it asks for the sum of fewer numbers.
Therefore, the answer must be less than 23,104, so (E) can
be eliminated. The numbers that are not to be included in
the answer sum are 1 and 303. Subtract these from 23,104
to get the new sum. 23,104 – 1 = 23,103 – 303 = 22,800.
Choice (C) is the credited response.
18. E To determine if the intervals satisfy the inequality, pick a
value from each one and plug it in for c into the equation.
For case I, try c =− . The inequality becomes
=

. This is not less than

0, so case I is not true. Choices (A) and (D) can be
eliminated, as they contain case I. For case II, plug in c =
− . The inequality becomes

. This

is less than 0, so case II satisfies the inequality. Choice (C)
can be eliminated, as it does not contain case II. For case III,
plug in c =− . The inequality becomes
. This is less than 0, so case III is

also true, and (E) is the credited response.
19. B When asked for the number of values that are possible for a
variable, start Plugging In, following the requirements of
the question. The first positive integer is 1, and there is no
integer power to which 1 can be raised that will make it
equal 81. The same is true if f = 2. If f = 3, it could be
raised to the 4th power to yield 81. In fact, if 81 is broken
down into prime factors, the only one is 3. Therefore, trying
only multiples of 3 can save time. If f = 6, there is no
integer power to which it can be raised that will make it
equal 81. If f = 9, it could be raised to the 2nd power to
yield 81. At this point, the values possible for g are getting
very small. Rather than plugging in for f, now try plugging
in for g with the only remaining positive integer, which is 1.
If f1 = 81, then f = 81. There are no more positive integer
combinations of f and g that will make the equation true, so
there are only 3 values for f: 3, 9, and 81. Therefore, (B) is
the credited response.
20. C When the question has variables in the answer choices, Plug
In. Pick values for r and s, such as r = 2 and s = 8 With
these values, point M is now at (2, 8) and point N is at (6,
0). Draw a sketch of these points in the coordinate plane
and the triangle they form with the origin.

To find the area of the triangle, write out the formula: A =
bh and plug in known values. The base is 6 and the height
is 8, so the area is

(6)(8) or 24. This is the target number.

Now plug r = 2 and s = 8 into the answer choices to see
which matches this target number. Choice (A) is

(2)(8),

which equals 8. This is not the target answer, so (A) can be
eliminated. Choice (B) is (2)(8) or 16, so it can also be
eliminated. Choice (C) is (2)(8), which equals 24. This is
the target answer, but the remaining answers must be
checked before selecting (C). Choice (D) is

(23)(8), which

equals 32, so (D) can be eliminated. Choice (E) is (23)(8),
which equals 64, so (E) can be eliminated. Choice (C) is the
only one remaining and is the credited response.

Section 3
25. B Start with the first blank. Since Stephen’s new road bike is
described as lighter, look for a word that means lighter.
Eliminate everything but choices (A) and (B). Since his new
bike is lighter, his previous bike would have been “heavy.”
Eliminate choice (A) since speedy is irrelevant. Choice (B) is
the correct answer.
26. D Start with the second blank. Since the sentence states that
the deli doesn’t do something properly anymore, it must be
“difficult” to distinguish a strip steak from a pot roast.
Eliminate everything but choices (D) and (E). Next, check
the first blank. Since it’s difficult to distinguish the meats,
they must not be “labeled” properly. Restock doesn’t match
“labeled,” so eliminate choice (E). Choice (D) is the correct
answer.
27. E Since the folk singer showcased the human spirit in all its
forms, look for a word similar to “emphasize” that would fit
the blank. Eliminate choices (A) and (D) since these are the
opposite of emphasize. Choice (B) means to “express
coherently,” which doesn’t quite fit. Eliminate choice (C)
since it means to “give human qualities to ideas or
concepts.” Choice (E) works, since underscore means to
“show importance to,” which is similar to emphasize.
Choice (E) is the correct answer.
28. A Start with the first blank. Since it’s stated that the new work
has many elements that are out of place, look for a word that
means out of place. Choice (A) is a good match for out of
place and choice (D), which means “old fashioned,” could
also fit, so eliminate choices (B), (C), and (E). Next, check

the second blank. Since elements or details are out of place,
look for a word similar to “context” for the second blank.
Eliminate choice (D) since whimsy doesn’t fit. Choice (A) is
the correct answer.
29. E The sentence tells us that Reinhold was always backing down
from his own arguments and deferring his point of view, so fill
in the blank with something like “giving in to others.”
Eliminate choices (A) and (C) since both mean the opposite
of the clue. Choice (B) means “brief” and choice (D) means
“persistence,” so eliminate them. Choice (E) matches the
clue, therefore it is the correct answer.
30. C The correct answer to this question must address both
passages, so be wary of answers that are one-sided.
Eliminate choice (A) since all fans is extreme. Choice (B)
also doesn’t work since neither passage ever states that
sports fanaticism is unhealthy. Choice (C) could work since
Passage 1 mentions that the author’s family’s eyes roll
whenever he would talk about sports, and the author of
Passage 2 mentions that his knowledge is met with derision.
Eliminate choices (D) and (E) since both elation and
contempt are too strong. Choice (C) is the correct answer.
31. E The author of Passage 1 sees his family’s eyes roll when he
talks about sports, and the sports fanatics in Passage 2 are
similar to the author of Passage 1, so the family would not
be interested in the view of the sports fanatics of Passage 2.
Choices (A), (C), and (D) all indicate some form of
acceptance, so eliminate them. Choice (B) is too extreme.
Choice (E) fits well and is therefore the correct answer.
32. A This is a vocabulary in context question, so cross out the
word in question and replace it with another word. Since
knowing the rules of Australian football seems to be
something only the author cares about, we can replace

garnered with “gained” or “accumulated.” Only choice (A)
fits, so it is the correct answer.
33. E The correct answer to this question must address both
passages, so be wary of answers that are one-sided. Choice
(A) is incorrect since it doesn’t apply to either passage.
Eliminate choices (B) and (D) since only Passage 2 makes
any sort of comparison or hypothetical situation. Passage 1
makes use of personal experience, but Passage 2 does not, so
eliminate choice (C). Choice (E) fits because Passage 1
refers to why a Wing T formation is preferable to a Double
Back and Passage 2 mentions who played center field for the
winning team of the 1974 World Series. Choice (E) is the
correct answer.
34. E The first two lines of the passage contain the following:
Daddy was seeing an awful lot of his new friend. One of the
rooms in his house was all of a sudden full of her stuff. We
don’t know yet how the young girl is assessing the situation,
so choice (E) is the only one of the choices with the
appropriate amount of support in the passage. The other
choices suggest that the girl is disapproving of her father’s
new friend, a claim that is not supported in the passage.
35. E The third line of the passage contains the following: It had
started with a few dinners and shopping trips, and now it
seemed that their father’s friend basically lived in the house,
even shifting around some furniture that had been in place for
as long as Sarah could remember. The word basically suggests
that Tess does not literally live in the house but that she
spends as much time there as one who does live there,
which is reflected in choice (E). The other choices contain
some words from the passage, but the information in those
choices is not supported in the passage.
36. B The third line of the passage contains the following: It had

started with a few dinners and shopping trips, and now it
seemed that their father’s friend basically lived in the house,
even shifting around some furniture that had been in place for
as long as Sarah could remember. The idea of shifting around
some furniture is offered as evidence that their father’s friend
basically lived in the house. It can be inferred, therefore, that
shifting around furniture is something that is typically done
by someone who lives in the house containing that
furniture, as choice (B) suggests. Because the passage moves
between ideas quickly, it doesn’t say anything else about
Sarah’s perspective on this furniture moving, so none of the
other answer choices are supported in the passage.
37. D In the first three sentences of the second paragraph, there
are a number of words that imply a change: then, became,
now, eventually, introduced. The quotation marks are
evidence of that change, with the older people in the story
now referring to themselves as part of Sarah’s family, as
choice (D) suggests. The words in quotes are not meanspirited or slangy, eliminating choices (A) and (C), and
nothing in the passage suggests that any of these terms are
metaphorical, eliminating choice (E).
38. B The first two paragraphs of the passage explore Sarah’s
confusion over the more-frequent presence of her father’s
“new friend.” Tess surprises Sarah after school one day to
take her shopping for a Junior Bridesmaid’s dress. Tess is
surprised by the announcement, wondering Bride?, because
she has not yet understood that Tess and her father are to
be married. Choice (B) paraphrases this idea. Choices (A),
(C), and (E) are too literal and are not supported in the
passage. And although Sarah is not fully used to the idea of
having Tess as a mother, she does not necessarily “resist” it,
eliminating choice (D).
39. B The seventh paragraph states, In the coming weeks, though,

Sarah was not to be so involved again. She was usually asked to
watch her brother as her daddy and Tess met with planners,
caterers, and decorators. A series of questions follows,
outlining the kinds of questions they might be asking these
planners, caterers, and decorators, or naming the specific
topics of their meetings with these wedding assistants, as
choice (B) implies. The particular questions are not relevant
to the larger idea of the story (a young girl coming to terms
with her father’s remarriage), so the other choices can be
eliminated.
40. D The sentence listed in the question states the following:
Sarah had never seen him so calm—he was usually such an
over-planner, barking orders at all within his sight. There is a
contrast here between her father’s current calm and the fact
that he is usually barking orders. Therefore, the answer must
be the opposite of calm, as only choice (D) is.
41. C Sarah is asked to watch her brother as Tess and her father
plan their wedding. She tries to eavesdrop subtly, but as her
father’s question implies, he is aware that she is listening to
the conversation. Because the question immediately shifts
back to Sarah’s perception, we know little else about what
the father thinks. Only choice (C) works, therefore, and the
others can be eliminated.
42. C Toward the end of the passage, Sarah wishes more and
more to be involved with her father’s wedding: She wanted
to walk in there and take a seat at the table with them. And
later, She wanted to be at the table, calling whatever shots she
could. There are hints of the other answer choices, but none
has the textual support of choice (C).
43. C The first sentence says the following: Online education hasn’t
freed itself of all the connotations, both positive and negative,
that anything “online” could have. In other words, online

education has both positive and negative features, or both
good and bad aspects, as choice (C) indicates. The other
choices may be common ideas about online education, but
they are not supported in the passage.
44. C The previous sentence states, On the other hand, online
education is, as much as any other product, a child of the
market. The sentence referred to in the question expands on
this idea, as choice (C) indicates, stating the market benefits
of online education. Although the sentence reflects the
speech of administrators, it does not mock them, and it is
not meant to sell the product to the reader, eliminating
choices (A) and (D).
45. E Of face-to-face education, the author of Passage 1 states the
following: Perhaps the problem is deeper. Maybe “online”
education is not such a new development: those students who
are in face-to-face classes are not required to do their
homework in Internet-free areas, and most students can browse
the Internet freely in class. The Internet is already everywhere,
and the undetected outcome may be lowered educational
standards in general. The author of Passage 2 states the
following, The “real thing,” after all, had its own set of
problems long before online education came along, and while
students may be truant or distracted from online courses, they
are just as likely to be so in face-to-face courses. Both authors,
therefore, suggest that face-to-face education is imperfect
and susceptible to many of the same influences as online
education, lending support to choice (E).
46. E Cross out the word in question, and fill in the blank with
your own. The word appears in the following line: And the
belief that online education must be a _______ form of the “real
thing” is simply misguided conservatism. A term like watered
down or a word like lesser would work here. While choices
(B) and (C) may have meanings similar to diluted, only

choice (E) works in this context.
47. A The author of Passage 1 outlines the problem as follows:
those students who are in face-to-face classes are not required
to do their homework in Internet-free areas, and most students
can browse the Internet freely in class. The Internet is already
everywhere, and the undetected outcome may be lowered
educational standards in general. This agrees almost exactly
with what the author of Passage 2 has to say, so the authors
are essentially in agreement, as choice (A) suggests. While
the author of Passage 1 might consider the lines in Passage
2 respectful, there is no reason to believe that she would
consider them exceedingly so.
48. B The author of Passage 1 writes, So how successful have these
online courses been? According to a 2013 study, 77 percent of
academic leaders rate the learning outcomes in online education
as the same or superior to those in face-to-face classes. The
author of Passage 2 cites the same statistic, after stating,
Online education certainly has its benefits. Both sentences
reflect the benefits of online education as perceived by
educators, lending support to choice (B). While online
education may help these teachers to achieve their learning
objectives, the authors do not bring up this statistic in order
to discuss these learning objectives, but rather to show how
effective teachers consider online learning, eliminating
choice (E).

Section 4
21. D PITA! Start with choice (C), plugging in 4 for t. The first
equation is then 4 < 6, which is true, and the second is 16
< 16, which is not true. Eliminate choices (C), (B), and (A)
and go bigger. Try choice (D), plugging in 5 for t. The first
equation is then 5 < 6, which is true, and the second is 16
< 20, which is also true. Since both equations are true, t =
5. The credited response is (D).
22. A Be safe: Plug In. Plug in 6 for the side of the square and
label all of the sides 6. W, X, and Y are the midpoints, so
label AW, WB, BX, XC, CY, and YD each as 3. Now BC = 6.
Check all of the answer choices to find the one that does
NOT equal 6. Choice (A) is AD + AW = 6 + 3 = 9. Choice
(B) is AW + XC = 3 + 3 = 6. Choice (C) is CD = 6.
Choice (D) is DY + BW = 3 + 3 = 6. Choice (E) is AD =
6. The credited response is (A).
23. B Solve for z. First subtract 6 from both sides of the equation
to get 4z = 14. Then divide both sides of the equation by 4
to get z =

. That is the only solution to the equation. The

answer is (B).
24. C PITA! Start with (C), plugging in 5 for t. First, use the
second equation to find
= s. Use the calculator and find
that s is approximately 2.24. Then plug in 2.24 for s in the
second equation. Since 10 < 11.2 < 12, t could equal 5.
The credited response is (C).

25. D The total surface area of the solid is equal to the sum of the
areas of all the individual faces. First, count the faces. There
are 6 squares on the top, and therefore 6 on the bottom.
There are 2 squares on the front, and therefore 2 on the
back. There are 3 squares on the side, and therefore 3 on
the other side. Thus, there are a total of 6 + 6 + 3 + 3 +
2 + 2 = 22 squares. Since each square has an area of 3
square inches, the total surface area is 22 × 3 = 66 square
inches. The credited response is (D).
26. E Variables in the answers: Plug In! Since x > 0, choose a
positive number for x; in this case, x = 2. Since is negative,
choose a negative number for y; in this case, y = –8. Check
each answer choice to find which one is a negative number.
(A) is (2)3 = 8; eliminate it because it’s positive. (B) is (–
8)2 = 64; eliminate it because it’s positive. (C) is –(–8) =
8; eliminate it because it’s positive. (D) is 2(2) = 4;
eliminate it because it’s positive. (E) is –8; keep it because
it’s negative. The credited response is (E).
27. B Express the probability as a fraction:
total number of degrees in a circle is 360, so

. The
.

Solve to find that the red sectors have a total of 90°. There
are two red sectors that each have a degree measure of r, so
divide 90 by 2 to find that r = 45°. The credited response is
(B).
28. C First, use the table to find h(1). When the x column is 1 the
h(x) column is 3, so h(1) = 3. Since g(x) = h(1), g(x) = 3.
Now use the table to find the x value. When the g(x)
column is 3, the x column is 2, so x = 2. The credited

response is (C).
29. 6 Plug in any of the (x, y) pairs from the table into the
equation. The last (x, y) pair in the table is (–2, –3), so –2
=

. Multiply both sides of the equation by –3 to find that

k = 6.
30. 187 Kevin makes 8 dollars for each chore, so divide 1,500
dollars by 8 to find the number of chores. 1,500 ÷ 8 =
187.5, which is not an integer. Round up or round down?
Try both to be safe. 188 chores times 8 dollars per chore
equals 1,504 dollars, which is too big. 187 chores times 8
dollars per chore equals 1,496 dollars, which is less than
1,500.
31. 50 The lines are parallel, so all the big angles are equal and all
the small angles are equal, and big + small = 180°. The
small angle is 30°, so the big angle is 180° – 30° = 150°.
The big angle is labeled 3x, so 3x = 150°. Divide both sides
by 3 to find that x = 50°.
32. 384 If 36% of the juniors selected “Go to the beach” then the
remaining 64% of the juniors selected a response other than
“Go to the beach.” 64% of the 600 total juniors is

×

600 = 384.
33. 22 Write the area formula: A = πr2. The area of circle P is
121π, so 121π = πr2 and r = 11. The diameter is twice the
radius, so d = 2r = 2 × 11 = 22.

34.

36 or 72
First find that 12 ´ 9 = 108. Is 108 a factor of z? To find z,
first list the multiples of 12 and the multiples of 9 up to
120. The multiples that 12 and 9 have in common are
possible values of z.
Multiples of 12: (12, 24, 36, 48, 60, 72, 84, 96, 108)
Multiples of 9: (9, 18, 27, 36, 45, 54, 63, 72, 81, 90, 99,
108, 117)
Therefore, the possible values of z are 36, 72, and 108. 108
is not a factor of 36; it is a possible answer because it
proves the statement false. 108 is not a factor of 72; it is a
possible answer because it proves the statement false. 108 is
a factor of 108; it is not a possible answer because it proves
the statement true.

35. 44 To find the shaded area, subtract the three small triangles
from the large triangle. Write the area formula: A =

bh.

The base of the large triangle is the sum of the bases of the
small triangles. Use the formula to find the base of each
small triangle. Each of the triangles is an isosceles right
(45:45:90) triangle, so the base and the height are equal.
Thus the formula can be written as A =
b2. Solve for the base of triangle A:

b × b or A =

b2 = 18 then b2 = 36,

so b = 6. Solve for the base of triangle B:

b2 = 8 then b2

= 16, so b = 4. Solve for the base of triangle C:

b2 = 2

then b2 = 4, so b = 2. The base of the large triangle is 6 +
4 + 2 = 12 and so the area of the large triangle is A = 1
22 = 72. The sum of the areas of the small triangles is 18
+ 8 + 2 = 28. Subtract the unshaded area from the large
area to get the shaded area: 72 – 28 = 44.
36.

or .083
Plug In! Plug in a = 4 and b = 5 to make the first equation
true. Now plug in a = 4 the second equation to find c:
so c = 60. Therefore,

. (Note:

would also be counted as a correct answer.)
37. 252 Write out the pattern and then extrapolate. List the numbers
from 100 to 199 that have at least one digit that is a four.
{104, 114, 124, 134, 140, 141, 142, 143, 144, 145,
146,147, 148, 149, 154, 164, 174, 184, 194}. There are 19
numbers in the one-hundreds that have at least one four.
The same will be true of the two-hundreds, three-hundreds,
five-hundreds, six-hundreds, seven-hundreds, eighthundreds, and nine-hundreds. So far that’s 19 ´ 8 = 152
numbers with at least one four. Then there are the fourhundreds: all 100 numbers from 400 to 499 have at least
one four. So add that to the total to get 152 + 100 = 252.
38. 60 This problem can be tackled as a rate problem using the

formula or as an average problem using the average pie.
Either way, set up an equation or a pie for both Ben and
Carl. Since they both drove for the same amount of time, set
your equation equal to time: time =

. If b represents

the distance Ben drove, and he drove 15 miles further than
Carl did, the distance Carl drove is b – 15. Therefore, the
equation for Ben is t =

and the equation for Carl is t =

. The times are equal so set the two equations equal
to each other:

=

. Cross multiply and solve for b:

20b – 300 = 15b, then 5b = 300, so b = 60.

Section 5
1. D The phrase, The Great Wall of China, which was built to
protect the Chinese Empire from invasion is an incomplete
thought. Since a comma combined with the word and can
only be used to connect two complete thoughts, this
sentence does not correctly connect the two ideas. Eliminate
choice (A). Choice (B) makes both the first and the second
thoughts complete, but connects the two with a comma.
Therefore, choice (B) contains a comma splice error. In
choice (C), the thought The Great Wall of China, built to
protect the Chinese Empire from invasion is an incomplete
thought. The phrase therefore extending over more than
13,000 miles is also incomplete. This choice contains two
incomplete ideas that do not form a complete thought even
when combined, so choice (C) is incorrect. In choice (E),
the phrase it was built to protect the Chinese Empire is set off
by commas, and should therefore contain unnecessary
information. However, if you remove that part of the
sentence, then the remaining thought is, The Great Wall of
China … extending over more than 13,000 miles. This is an
incomplete thought, so choice (E) does not contain a
complete sentence, and is therefore incorrect. Choice (D)
fixes the error in the original sentence and does not
introduce any new errors, so choice (D) is the correct
answer.
2. B This sentence uses ignoring, rather than ignore, and therefore
contains an incomplete thought. Choices (A), (C), and (E)
all repeat the error in the original sentence and are
therefore incorrect. Choice (D) adds the word who, which
also makes the sentence incomplete. Therefore, the correct
answer is choice (B), which fixes the original error and does

not introduce any new errors.
3. E The modifying phrase Walking on the moon’s surface for
slightly more than two and a half hours should describe Neil
Armstrong and Buzz Aldrin, since those two men were the
individuals who did the walking. However, as it is currently
written, the phrase describes numerous photos, since that
phrase appears immediately after the comma. Therefore,
this sentence contains a misplaced modifier error. Neil
Armstrong and Buzz Aldrin should appear immediately after
the comma, so eliminate choices (A), (B), and (C). Choice
(D) incorrectly places the prepositional phrase of Little West
Crater after took, and is therefore incorrect. Choice (E) fixes
the original error and does not introduce any new errors, so
choice (E) is the correct answer.
4. A The way the sentence is currently written, the underlined
verb phrase agrees with the non-underlined parts of the
sentence in both number and tense, so choice (A) does not
contain an error. Choice (B) adds a conjunction, although, to
the beginning of the verb phrase and changes the form of
the verb to gaining. This causes the entire sentence to
become a fragment, so eliminate choice (B). Choice (E)
repeats this same error, so eliminate choice (E) also. Choice
(C) uses a comma and the word but to connect the two ideas
in the sentence. However, only two complete ideas can be
connected using a comma and the word but. Since
Chiropractic methods of treatment, once commonly criticized by
many in the medical field, is not a complete idea, it cannot be
connected to the second half of the sentence using a comma
and the word but. Eliminate choice (C). Choice (D)
inappropriately changes the tense of the verbs by adding
the future tense verb will, so choice (D) is also incorrect.
Choice (A) is the correct answer.
5. C The verb is is singular, but the subject of the sentence is

rainforests, which is plural. Therefore, this sentence contains
a subject-verb agreement error. Eliminate choice (A).
Choice (B) introduces the word that, which makes the
sentence incomplete, so choice (B) is not the credited
answer. Choices (D) and (E) incorrectly change the tense of
the sentence, and are therefore not the credited answers.
Choice (C) correctly changes the verb to the plural verb are
and is the correct answer.
6. D This sentence contains two complete thoughts joined by a
comma, which is a comma splice error. Choices (A), (B),
and (C) repeat this error and are therefore incorrect. Choice
(E) uses the singular verb was, but the subject of the verb is
mutated cells, ulcers, and cancer. Since the verb is singular
and the subject is plural, this choice contains a subject-verb
agreement error. Choice (D) fixes the error in the original
sentence and does not introduce any new errors. Therefore,
choice (D) is the correct answer.
7. B This sentence contains the modifying phrase Though most
famous for her relationship with Beatles singer John Lennon.
This phrase should describe whatever appears after the
comma. However, the phrase the important contributions,
rather than Yoko Ono, appears after the comma. Therefore,
this sentence contains a misplaced modifier. Both choices
(A) and (D) repeat this error in the same way. In choice (C),
the phrase Yoko Ono’s important contributions, rather than
Yoko Ono, appears right after the comma, so choice (C) also
has a misplaced modifier error. In choice (E), the phrase the
works of Yoko Ono appears after the comma, so choice (E)
also has a misplaced modifier error. Only choice (B) fixes
the error in the sentence.
8. A This sentence indicates that Genghis Khan did two things:
he united … tribes, and founded the Mongol Empire. Since this
sentence contains two verbs in a list, the verbs should be in

the same form. As the sentence is currently written, the
verbs are parallel, so keep choice (A). Choice (B) uses the
word who. Since the word that appears immediately before
the comma is century, this choice suggests that it is the
century, not Genghis Khan, that founded the Mongol
Empire. Thus, choice (B) is incorrect. Choice (C) uses the
verb found, which is not parallel with united, so choice (C)
creates a parallelism error. Choice (E) also creates a
parallelism error by pairing united with founding. Eliminate
both choice (C) and choice (E). Choice (D) adds a subject to
the second half of the sentence, thus turning that part of the
sentence into a complete thought. Therefore, choice (D)
contains two complete thoughts joined by a comma.
Eliminate choice (D), since it has a comma splice error.
Choice (A) is the correct answer.
9. E As written, the verb demonstrated does not agree with the
verb prepares in tense. Both verbs should be in present
tense, so eliminate choice (A). Choices (B) and (C) use the
singular pronoun it to refer to the plural noun classes, so
both of these choices are incorrect. Choice (D) initially uses
the plural pronoun they, but switches to the singular
pronoun it later in the sentence. Thus choice (D) is
incorrect. Choice (E) correctly uses plural pronouns to refer
to classes and uses the correct verb tenses. Thus, choice (E)
is the correct answer.
10. E This sentence provides three verbs in a list: chose, discovered,
and was postponed. However, items in a list should be
parallel. In this case, the last verb in the list is not in the
same form as the other two verbs. Therefore, this sentence
contains a parallelism error. Choices (A), (C), and (D) all
contain similar parallelism errors and are therefore
incorrect. Choice (B) is also not parallel, because even
though the verb is in the correct form, the choice also

includes the subject she, unlike the second verb in the list.
Choice (B) is also missing the conjunction and, which is
needed before the last item in the list. Only choice (E) fixes
the original error and does not introduce any new errors.
11. D The words simultaneously and as well are redundant, so
choice (A) is not the correct answer. Choice (C) repeats the
error in the original sentence. Since the phrase Ludovic built
an enormous house of cards is a complete thought, and it was
simultaneously very fragile is also a complete thought, you
cannot join the two thoughts with a comma. Therefore,
choice (B) contains a comma splice error. Choice (E)
changes the direction of the sentence by using and rather
than but. Since the two ideas in the sentence—that the
house was enormous and that the house was fragile—are
opposite direction ideas, they should be joined with a
conjunction that signals that they are opposites. Choice (D)
fixes the redundancy error, so choice (D) is the correct
answer.
12. B The verb wore is in past tense, but the verb start is in present
tense. Since nothing in the sentence indicates that a change
of tense is required, this sentence contains a verb tense
error. Eliminate choice (A). Choice (C) repeats the error in
the original sentence and is therefore not the correct
answer. Choice (D) uses the present perfect had started
dropping. When a verb refers to something that began in the
past and is still happening, the present perfect tense is
appropriate, but this sentence refers to an event that
occurred entirely in the past, so choice (D) is not the correct
answer. Choice (E) uses are beginning to drop, which would
also refer to an event happening in the present, rather than
in the past, so choice (E) is incorrect. Choice (B) correctly
uses the past tense, and does not introduce any new errors,
so choice (B) is correct.

13. C In the original sentence, the phrase originally a railroad
bridge and part of the Poughkeepsie Bridge Route is set off by
commas, so the phrase should contain unnecessary
information, and the sentence should make sense without it.
Notice that if you eliminate the phrase, you are left with
Walkway Over the Hudson, now used by locals as a pedestrian
walkway. The main subject is Walkway Over the Hudson, but
the subject is missing a verb, and the sentence is a
fragment. Eliminate choice (A). Choice (B) uses the word
which, and therefore changes the meaning of the sentence so
that the phrase is now used by locals as a pedestrian walkway
applies to the Poughkeepsie Bridge Route rather than to
Walkway Over the Hudson. It also creates a fragment. Choice
(C) adds the verb is, and therefore makes the sentence
complete. Eliminate choice (D), since it contains the word
being. Choice (E) connects the thoughts Walkway Over the
Hudson, originally a railroad bridge and used today by locals as
a pedestrian walkway and it was once part of the Poughkeepsie
Bridge Route with a comma and the word and. However, in
order to join two thoughts with a comma and the word and,
both thoughts must be complete thoughts. Since the first
thought is incomplete, this sentence does not correctly join
the two thoughts. Eliminate choice (E). Choice (C) remains
as the best answer.
14. B The original sentence compares gecko’s feet to other lizards.
Since the sentence should compare lizard’s feet to other
lizard’s feet or geckos to other lizards, but not feet to lizards,
there is a comparison error. Eliminate choice (A). Choices
(D) and (E) contain similar comparison errors, and are
therefore incorrect. Choice (C) correctly fixes the
comparison error so that the sentence compares gecko’s feet
to other lizard’s feet, but now the phrase such as the iguana or
the Komodo dragon modifies other lizard’s feet. Since the
iguana and the Komodo dragon are examples of lizards,

rather than of lizard’s feet, this choice changes the meaning
of the sentence, and is therefore not the correct answer.
Since choice (B) correctly fixes the original error and does
not introduce any new errors, it is the correct answer.
15. D The correct idiom is similarities between one thing and another
rather than similarities between one thing with another.
Therefore, this sentence contains an idiom error. Choices
(A) and (B) repeat the original error and are therefore
incorrect. The sentence should compare the results of the
biologist’s experiments to the results of Watson and Crick’s
experiments. However, choices (C) and (E) compare the
results of the biologist’s experiments to the experiments of
Watson and Crick. Since these choices compare results to
experiments rather than results to results, these choices
contain comparison errors. Choice (D) fixes the original
error in the sentence and does not introduce any new
errors, so choice (D) is the correct answer.
16. D In the original sentence By planning is redundant with why,
since both indicate a reason. Therefore, choice (A) is
incorrect. In choice (B), the subject is his planning and the
verb is ended. Since Carl, not the planning, is the one who
actually did the action in the sentence, choice (B) puts the
sentence into the passive voice, and is therefore incorrect.
Choice (C) uses plan of arriving; however, the correct idiom
is plan to rather than plan of. Thus, choice (C) contains an
idiom error. Choice (E) incorrectly uses He planned as the
subject of the verb is. However, the phrase He planned
already contains a subject and a verb, so it cannot be used
as a subject. Choice (D) fixes the original error in the
sentence and does not introduce any new errors, so choice
(D) is the correct answer.
17. C The correct idiom is not only … but also. The original
sentence uses not only … but, and omits the also. Therefore,

this sentence contains an idiom error. Eliminate choice (A).
Choice (B) makes a similar error by omitting but and is also
incorrect. According to choice (D), the sentence lists two
reasons that Tesla was remarkable: because he made
numerous contributions toward the fields of x-ray imaging and
radio and because he patented also more than 300 inventions.
When you have items in a list, those items should be
parallel. With the placement of also in the second part of
the list, the items are not parallel, so choice (D) is incorrect.
Choice (E) is similarly not parallel because the first item in
the list uses because, whereas the second does not. Choice
(C) fixes the error in the original sentence, and does not
introduce any new errors, so choice (C) is the correct
answer.
18. A The clause Alzheimer’s disease causes memory loss and
confusion is a complete thought. The clause for instance,
those affected frequently forget the names of close friends and
relatives is also a complete thought. These two thoughts are
correctly joined by a semicolon, so choice (A) does not
contain an error. Choices (B) and (E) change the intended
meaning of the sentence by implying that Alzheimer’s
disease, rather than those affected by Alzheimer’s disease,
frequently forgets the names of close friends and relatives,
so both choices are incorrect. Choice (C) uses a semicolon
to connect the two thoughts in the sentence. However, a
semicolon connects two complete thoughts, and the phrase
for instance, often forgetting the names of close friends and
relatives is not a complete thought. Choice (D) connects two
complete thoughts with a comma, so choice (D) contains a
comma splice error and is incorrect.
19. E The original sentence uses finishing, rather than finished, and
thus does not contain a complete thought. In choice (B), the
clause In 1505, Michelangelo started building Pope Julius II’s

tomb is a complete thought. The clause however, it was never
finished to his satisfaction, perhaps because he was constantly
distracted by other tasks is also a complete thought. Since
this choice joins two complete thoughts with a comma, this
choice contains a comma splice error. Choice (D) also
contains two complete thoughts joined by a comma, and
therefore repeats the error in choice (B). In choice (C), the
modifying phrase although distracted, perhaps, by other tasks
should describe whatever appears immediately after the
comma. However, since it, rather than he appears
immediately after the comma, this choice suggests that the
Pope’s tomb, rather than Michelangelo, was distracted. This
choice contains a modifier error and is therefore incorrect.
Choice (E) corrects the error in the original sentence and
does not introduce any new errors, so choice (E) is the
correct answer.
20. B The subject of the sentence is claims, which is plural, and
the main verb is has convinced, which is singular. Therefore,
this sentence contains a subject-verb agreement error.
Choices (A) and (C) repeat this error, and are therefore
incorrect. Choice (D) changes the intended meaning of the
sentence by making it seem as though the claims of the
witnesses, rather than the jury, returned a verdict of guilty.
Choice (E) uses they, which is plural, to refer to jury, which
is singular. Therefore choice (E) contains a pronoun
agreement error. Choice (B) fixes the original error in the
sentence, and does not introduce any new errors, so choice
(B) is the correct answer.
21. B This sentence uses having been outweighed, rather than have
been outweighed, and therefore does not contain a complete
thought. Therefore, the correct answer is choice (B).
22. C The pronoun her is part of the plural subject her and Tiffany.
However, her cannot be the subject of the sentence, because

it is an object pronoun; she is the appropriate subject
pronoun. Thus, choice (C) contains a pronoun error.
23. B This sentence uses the present perfect verb have been
received, which suggests that the action in the sentence
started in the past and is continuing in the present.
However, the sentence begins with the phrase when the
impressionists began, which indicates that the action
occurred in the past. Therefore, choice (B) should not be in
the present perfect tense, and contains a verb tense error.
24. B This sentence uses which to refer to Mao Zedong, who was a
person. However, who refers to people, and which refers to
things. Therefore, choice (B) contains an error and is the
correct answer.
25. B This sentence lists two reasons that the grey squirrel has
hidden nuts and seed: to ensure its food source and preventing
other competing species from consuming all of the available
food. The verbs ensure and preventing are not in the same
form. Thus, choice (B) contains a parallelism error.
26. A This sentence couples the word both with the phrase as well
as. However, the correct idiom is both … and. Therefore,
choice (A) contains an idiom error, since the phrase as well
as should be replaced by the word and.
27. B The correct idiom is responded to, rather than responded at.
Therefore, choice (B) contains an idiom error.
28. D The subject of the sentence is prevalence, which is singular.
However, the verb is have increased, which is plural.
Therefore, choice (D) contains a subject-verb agreement
error.
29. B This sentence uses having as the main verb in the sentence,

which makes the thought in the sentence incomplete.
Therefore, choice (B) contains a verb tense error, and is the
correct answer.
30. C This sentence uses the adjective quick to describe the
driver’s action of changing lanes. However, you must use
adverbs, rather than adjectives, to describe actions.
Therefore, quickly, rather than quick, is the correct
modifying word, and choice (C) is the credited answer.
31. E There is nothing in the sentence to indicate that there is
more than one claim, so choice (A) is correct. Choice (B) is
the correct verb form and tense. The singular verb is in
choice (C) agrees with the singular subject claim, so choice
(C) is correct. Choice (D) has a plural verb, are, but the
subject for that verb is objects, so choice (D) is also correct.
There are no errors, so the correct answer is (E).
32. E The possessive pronoun whose properly refers to Amy, who
possesses volleyball skills. Therefore, choice (A) does not
contain an error. Choice (B) is part of the present perfect
verb have respected. Since the respect began in the past and
continues in the present, the verb is in the correct tense.
The subject of the verb is I, which agrees with the verb, so
choice (B) does not contain a subject-verb agreement error.
Additionally, the verb is not in a list, so this choice does not
contain any parallelism errors. Therefore, eliminate choice
(B). Choice (C) uses the pronoun I. This sentence essentially
says that Amy … understands better than I do how to properly
serve and spike the ball, so the pronoun I is correct. The verb
do is an understood verb that does not need to be directly
written into the sentence. Since the pronoun in choice (C) is
in the correct case, choice (C) does not contain a pronoun
error. Finally, choice (D) uses the present tense verb serve.
Since this verb agrees with the subject I, and is parallel with
the verb spike, choice (D) does not contain an error. This

sentence does not contain any grammatical errors, so the
correct answer is choice (E).
33. B The correct idiom is means to rather than means in, and
protecting should be protect. Therefore, choice (B) contains
both an idiom and verb error, and is the correct answer.
34. D This sentence makes a comparison: their reception would be
less expensive than their friends. However, since the expense
of a wedding cannot be compared to people, this sentence
contains a comparison error. In order to correctly compare
the expense of Josh and Carla’s wedding to the expense of
their friends’ weddings, the sentence would need to read
less expensive than their friends’ weddings, or than those of
their friends.
35. B As it is currently written, sentence 3 does not contain a
complete thought, and is therefore a fragment. Thus, choice
(A) is not the credited answer. Choice (E) combines the
sentences, but turns the resulting sentence into an
incomplete thought and is therefore incorrect. Choices (B),
(C), and (D) all fix the original problem by combining the
two sentences. Of these three choices, (B) is the most
concise, and it does not introduce any new errors, so the
correct answer is choice (B).
36. A The first paragraph discusses the history of portrait painting
and uses one particular portrait painter as an example, and
the second paragraph begins by discussing the challenges of
portrait paintings. Thus, a phrase that ties these two
subjects together is needed to transition from one paragraph
to the next. Choice (B) mentions the focus on photographic
accuracy, which is not discussed in the first paragraph.
Thus, choice (B) is not the correct answer. Choice (C)
discusses the demand from subjects, which is not mentioned
in either the first or the second paragraph, so choice (C) is

incorrect. Since the paragraph does not contain any
discussion of how attractive people are, choice (D) does not
follow the flow of ideas in the paragraph and is therefore
incorrect. Choice (E) references the time required to
become a skilled painter, but this subject is not discussed in
either the first or the second paragraph, so eliminate choice
(E). Choice (A) refers back to the first paragraph by
referencing the fact that portrait painters have been popular
for centuries, and therefore creates a connection between
the first paragraph and the second. Thus, choice (A) is the
correct answer.
37. E As it is currently written, the sentence says that this is
profitable. However, it is not clear whether this refers to the
fact that Cézanne required so many sittings, or to the fact
that he could spend hours painting a single feature.
Therefore, the original sentence contains an error and
choice (A) is not the correct answer. The paragraph does
not discuss the fact that Cézanne painted Impressionist
works, so choice (B) is incorrect. Choice (C) uses the
incorrect past perfect verb had and is therefore not the
credited answer. Choice (D) uses the present perfect verb
has, which would imply that the action is still ongoing.
Since Cézanne is no longer painting, choice (D) is incorrect.
Choice (E) correctly modifies the sentence to clarify that it
was Cézanne’s meticulousness that paid off, so choice (E) is
the correct answer.
38. D The second paragraph ends by discussing the success of one
of Cézanne’s paintings, but the third paragraph begins by
discussing paintings that have not been well received.
Therefore, you need a sentence that connects these two
ideas. Choice (A) relates back to paragraph 2, which
discusses a famous artist, but it does not relate to paragraph
3. Therefore, choice (A) is not the correct answer. Since the

third paragraph does not discuss the amount of time
required to paint a portrait, choice (B) is incorrect. Choice
(C) makes a statement of fact, but does not relate to the
topics in either paragraph 2 or paragraph 3. Eliminate
choice (C). Choice (E) implies that the third paragraph will
prove something mentioned in the second paragraph to be
true. However, since paragraph 3 does not prove anything
from paragraph 2, choice (E) is incorrect. Choice (D)
connects the two paragraphs by introducing the idea that
not all portraits have been successful and, by using the
phrase so well received, referring back to the portraits
discussed in paragraph 2. Therefore, choice (D) is the
correct answer.
39. C As it currently reads, the sentence indicates that as a
portrayal … John Trumbull’s portrait … was rejected.
However, the painting was not rejected as a portrayal, but
was simply rejected. Therefore, in the original sentence, the
meaning is unclear. Choice (B) uses following, but since the
sentence is not discussing one thing that comes after
another, choice (B) is not the credited answer. Choice (D)
changes the intended meaning by suggesting that perhaps it
was the fact that the painting presented Washington at all
that caused the painting to be rejected, so choice (D) is not
the correct answer. Since the previous sentence discusses
flattering portraits, rather than accurate portraits, choice
(E) is incorrect. Choice (C) transitions from sentence 13,
which discusses the fact that flattering paintings are
sometimes rejected, to sentence 14, which gives an example
of a portrait that was rejected. Since the fact that the
painting of Washington was flattering relates the two
sentences, choice (C) is the correct answer.

Chapter 9
Practice Test 3

SECTION 1
Time — 25 minutes
24 Questions
(1-24)
Directions: For each question in this section, select the best answer from among the
choices given and fill in the corresponding circle on the answer sheet.

Each sentence below has one or two blanks, each blank indicating that something has
been omitted. Beneath the sentence are five words or sets of words labeled A through
E. Choose the word or set of words that, when inserted in the sentence, best fits the
meaning of the sentence as a whole.
Example:

Desiring to ------- his taunting friends, Mitch gave them taffy in hopes it would keep
their mouths shut.

(A) eliminate (B) satisfy (C) overcome (D) ridicule (E) silence

1. The gourmet restaurant was primarily known for its ------- cuisine, but the

dining room was rarely crowded due to the ------- demeanor of the wait staff.
(A) delectable . . exuberant
(B) unremarkable . . downbeat
(C) exciting . . dreary
(D) original . . primitive
(E) affordable . . inviting

2. Since the ------- of the honeybee population is currently underway, food

2. Since the ------- of the honeybee population is currently underway, food

production may be altered since these insects are ------- to this industry in the
United States.

(A) surging . . irrelevant
(B) flattening . . inconsequential
(C) renouncing . . robust
(D) declining . . vital
(E) pollinating . . anathemas
3. The Leaning Tower of Pisa, although regarded as one of the most remarkable
buildings in the world, is actually a ------- architectural effort since it
unintentionally tilts to one side.

(A) shoddy (B) superior (C) towering (D) repugnant (E) tumultuous
4. The early years of professional sports were ——– the basic concept of safety;

players hit and ran into each other with such careless abandon that it seemed
no one was interested in ------- play.
(A) cognizant of . . structured
(B) oblivious to . . cautious
(C) unaware of . . reckless
(D) presupposed to . . honest
(E) acclimated to . . considerate

5. Unlike an artist who works in the Photorealistic style, ------- to recreate every
single detail of the painting’s subject, an artist working in the Expressionist
style uses color to create an emotional impact.
(A)

endeavoring (B)

surrendering

disdaining (C)

loath (D)

collaborating (E)

6. In order to ------- a victory during the state science fair, the teacher only -------

6. In order to ------- a victory during the state science fair, the teacher only ------the work from her honors physics class.
(A) ensure . . capitulated
(B) cinch . . showcased
(C) sabotage . . presented
(D) snare . . assimilated
(E) transpire . . invited
7. The recent exploits of the daring adventurer did nothing to dampen the

public’s enthusiasm for his penchant for -------, but also confirmed that he had
no intention of worrying about his own safety.
(A)

cleverness (B)

imperilment

orthodoxy (C)

synergy (D)

profundity (E)

8. The actions of the criminal could only be described as -------; even after he was
convicted of his crime, he mean-spiritedly mocked and taunted his victims in
the courtroom
(A)

impetuous (B)

sanctimonious

indifferent (C)

extraneous (D)

pernicious (E)

The passages below are followed by questions based on their content; questions

following a pair of related passages may also be based on the relationship between the

paired passages. Answer the questions on the basis of what is stated or implied in the
passage and in any introductory material that may be provided.
Questions 9-10 are based on the following passage.

9. The author suggests that the “Naturalist literary movement” (line 4) was
(A) the most realistic literary period
(B) depressing for most readers
(C) a seemingly inevitable response to Romanticism
(D) pioneered by Stephen Crane’s Maggie, A Girl of the Streets
(E) primarily focused on the environment

10. In lines 8-12, the author mentions Maggie’s eventual suicide in order to

10. In lines 8-12, the author mentions Maggie’s eventual suicide in order to
(A) illustrate her unsatisfying family life
(B) suggest that her story would likely not appear in a Surrealist literary
novel

(C) indicate that many naturalist stories had tragic endings
(D) highlight how the Romantic movement was a more satisfactory literary
genre

(E) show how her environment played a greater role in her life than her
decisions

Questions 11-12 are based on the following passage.

11. Lines 1-3 (“The advent … past decade”) primarily serve to
(A) bemoan the spike in social media during the past several years
(B) introduce the differing consequences of these particular forms of
communication

(C) criticize those who use Twitter for selfish reasons
(D) celebrate technology and its effect on our environment
(E) consider the roles of social media and the Internet in our daily lives

12. The author uses the term “not ironically” in line 15 in order to

12. The author uses the term “not ironically” in line 15 in order to
(A) suggest that regime change was impossible without social media
(B) highlight the flippant attitude towards the revolution in Iran
(C) underscore that social media was integral to societal change
(D) show how narcissistic uses of social media pale in comparison with
those that have real consequences

(E) cast doubt on those who view the revolution in Iran as a result of
Twitter’s popularity

Questions 13-24 are based on the following passages.

13. Lines 3-5 (“In a … half”) suggest that the situation described should be

13. Lines 3-5 (“In a … half”) suggest that the situation described should be
considered

(A) rapid
(B) suspicious
(C) inevitable
(D) essential
(E) promising
14. The author of Passage 1 suggests that a “set of data” (line 10) should ideally
be

(A) taken from the same set as previous surveys
(B) diverse enough to reflect the group it represents
(C) randomly selected from a computer database
(D) made up of elementary-school-aged children
(E) comprised of equal numbers from each race
15. The author of Passage 2 would most likely argue that the “reach” (Passage 1,
line 15) is

(A) less representative of racial diversity than the author of Passage 1
promises

(B) more biased toward a particular gender than the author of Passage 1
hopes

(C) less relevant to the study than the author of Passage 1 believes
(D) drawn from a group that does not represent the diversity that the
author of Passage 1 assumes

(E) more similar to the reach of previous studies than the author of Passage
1 knows

16. The final paragraph of Passage 1 (lines 26-38) serves primarily to

16. The final paragraph of Passage 1 (lines 26-38) serves primarily to
(A) discount the survey’s findings by showing that they are already wellknown

(B) argue for a new approach that the survey’s results show is inevitable
(C) take issue with the statisticians who collected the data for the survey
(D) suggest the cultural implications of the trend it is describing
(E) offer an alternative conclusion based on the same set of data
17. The author of Passage 2 would most likely consider the final two sentences of
Passage 1 (lines 33-38) to be
(A) overstated
(B) ironic
(C) shrewd
(D) revolutionary
(E) dishonest
18. Which of the following would the author of Passage 2 most likely consider
another “apocalyptic” idea (line 40)?

(A) An editorial that argues that the trend toward text messaging has led to
a decline in the number of E-mails sent per year

(B) An article that shows that reading among teenagers has increased since
the popularization of e-readers

(C) A slideshow that details the 20 most environmentally conscious cities in
the United States

(D) A sociologist who argues that the use of smartphones among teenagers
will lead to a significant increase in driver fatalities

(E) A historical document that predicted that health care legislation would
be passed in the United States by the 1970s

19. Lines 55-64 (“It would … entirely’ ”) focus on which aspect of the “statistical

19. Lines 55-64 (“It would … entirely’ ”) focus on which aspect of the “statistical
certainty”?

(A) Its obviousness
(B) Its ridiculousness
(C) Its range
(D) Its conservatism
(E) Its bias
20. The author of Passage 2 indicates that the “landscape” referred to in line 66 is
(A) characterized by a lack of expertise
(B) based on regional preferences and racial identity
(C) filled with more appreciation of old favorites than anyone realizes
(D) shifting and thus not possible to describe
(E) no longer defined by its traditional parameters
21. In line 70, “crustiest” most nearly means
(A) most ineffective
(B) cruelest
(C) warmest
(D) most inflexible
(E) filthiest

22. The author of Passage 1 would most likely respond to the last statement in

22. The author of Passage 1 would most likely respond to the last statement in
Passage 2 (lines 79-82) by asserting that

(A) a survey of musical-education programs has broader cultural
importance

(B) classical music is as essential to well-rounded citizens as cursive
(C) Music in Peril is one of the first studies of school-aged children
(D) surveys like the one in Music in Peril are run by respected statisticians
(E) the average reader will be able to spot faulty data in any survey
23. Which best describes the tone of the first paragraph of Passage 1 and the tone
of the first paragraph of Passage 2, respectively?
(A) Morose vs. elated
(B) Alarmist vs. ignorant
(C) Sensitive vs. offensive
(D) Conservative vs. dismissive
(E) Concerned vs. skeptical
24. Which best conveys the primary relationship between the two passages?
(A) Passage 2 discusses some of the findings that undermine the survey
described in Passage 1.

(B) Passage 2 takes issue with some of the premises that shape the
argument made in Passage 1.

(C) Passage 2 offers the cultural context that adds support to the
conclusions drawn by the author of Passage 1.

(D) Passage 2 uses the predictions offered in Passage 1 as a way to argue for
a revolutionary change.

(E) Passage 2 provides new data that disproves the conclusions from the
survey discussed in Passage 1.

ST OP
If you finish before time is called, you may check your work on
this section only.
Do not turn to any other section in the test.

SECTION 2
Time — 25 minutes
20 Questions
(1-20)
Directions: For this section, solve each problem and decide which is the best of the
choices given. Fill in the corresponding circle on the answer sheet. You may use any
available space for scratchwork.

Notes
1. The use of a calculator is permitted.
2. All numbers used are real numbers.
3. Figures that accompany problems in this test are intended to provide information
useful in solving the problems. They are drawn as accurately as possible

EXCEPT when it is stated in a specific problem that the figure is not drawn to
scale. All figures lie in a plane unless other wise indicated.

4. Unless otherwise specified, the domain of any function f is assumed to be the set
of all real numbers x for which f(x) is a real number.

Reference Information

The number of degrees of arc in a circle is 360.
The sum of the measures in degrees of the angles of a triangle is 180.

1. If 2rst = 60 and st = 6, then r =

1. If 2rst = 60 and st = 6, then r =
(A)

2

(B)
(C)

5

(D)

6

(E) 45

2. What is the positive difference between (x + 5)2 and
(A) 36
(B) 56
(C) 78
(D) 81
(E) 84

when x = 4 ?

3. In the diagram above, circle N represents the set of all negative integers, circle
F represents the set of all multiples of 5, and circle E represents the set of all
even integers. Which of the following numbers would be in the shaded
region?

(A) –15
(B)

–8

(C)

7

(D)

25

(E)

30

4. Which of the following equations is satisfied by both n = 4 and n = 5 ?

4. Which of the following equations is satisfied by both n = 4 and n = 5 ?
I. 3n = 12
II. n2 – 9n + 20 = 0
III. (n – 4)(n – 5) = 0
(A) I only
(B) III only
(C) I and II only
(D) II and III only
(E) I, II, and III

5. In the figure above, O is the center of the semicircular region. What is the
value of a ?

(A) 12
(B) 24
(C) 30
(D) 36
(E) 42

6. One leg of the isosceles right triangle above is 6. What is the value of y ?
(A) 6
(B) 6
(C) 6
(D) 12
(E) 12

NUMBER OF HOURS HIGH SCHOOL ST UDENT S SPEND DOING HOMEWORK PER
NIGHT

7. The students at High School X were asked how many hours per weeknight they
typically spend doing homework, and the results are shown in the chart

above. Of the 800 students at this school, how many typically spend 3 hours
or more on homework per night?
(A)

56

(B)

64

(C) 160
(D) 200
(E) 296

8. If 2 < 2x – 6 < 4, which of the following could be the value of x ?
(A) –6
(B) –3
(C) 4
(D)
(E) 5

9. In the xy-plane above, the shaded semicircular region has an area of 18π.
What is the value of x ?
(A)

3

(B)

6

(C)

9

(D) 12
(E) 18

10. Jar L contains 196 pennies, jar M contains 184 pennies, and jar N contains 175

10. Jar L contains 196 pennies, jar M contains 184 pennies, and jar N contains 175
pennies. Pennies are to be transferred only from jar L to jar N. What is the

least number of pennies that must be transferred so that jar N will contain
more pennies than each of the other two jars?
(A) 11
(B) 12
(C) 13
(D) 14
(E) 15

11. In the left column of the table above, the first term of the sequence is 0 and
each term after the first is 7 more than the preceding term. In the right

column, the first term in the sequence is 12, and each term after the first is 4

more than the preceding term. If these sequences continue indefinitely, in how
many of the rows of the table will the terms for both sequences be equal?
(A) More than three
(B) Three
(C) Two
(D) One
(E) None

12. A woman is taking a cab ride to the airport. The fare consists of a one-time

12. A woman is taking a cab ride to the airport. The fare consists of a one-time
charge of $2.50 for the ride and a $3 charge for each mile traveled. If m

represents the number of miles travelled, which of the following represents
the total fare, in dollars, per mile?
(A) m + 2.50
(B) 2.50 + 3m
(C) 2.50m + 3m
(D)
(E)

13. Function g is defined such that there is exactly one value of x for which g(x) =
0. Which of the following could be the graph of function g ?
(A)

(B)

(C)

(D)

(E)

14. If one face of a rectangular solid is known to be a square, what is the greatest
number of faces of the solid that could be rectangles that are not square?
(A) Zero
(B) One
(C) Two
(D) Three
(E) Four

15. The table above shows the values for the function p. What is the value of 3p(4)
+ p(2) ?

(A) 6
(B) 8
(C) 12
(D) 18
(E) 24

Note: Figure not drawn to scale.
16. A game is played by dropping two pebbles, one onto each of the game boards

in the figure above. The score is the sum of the numbers in the regions where
the two pebbles land. The pebbles must land inside one of the numbered

regions, and it is equally likely that the pebbles will land in any one of the

numbered regions. What is the probability that the score will be at least 10 ?
(A)
(B)
(C)
(D)
(E)

17. In the circle above with center O, the average (arithmetic mean) of the areas

of the unshaded regions is equal to the sum of the areas of the shaded regions.
What is the value of z ?
(A)

45

(B)

60

(C)

90

(D) 120
(E) 135

18. Three points lie on a number line with coordinates f, g, and h such that f < g

< h. If f, g, and h are each integers, and fgh is a negative even integer, which
of the following must be true?
I. f < 0
II. gh > 0
III. f, g, and h are each even integers
(A) I only
(B) II only
(C) I and II only
(D) II and III only
(E) I, II, and III

19. Points M and N lie in the same plane. How many points in the same plane as
M and N could be 6 units from M and 2 units from N ?
(A) More than three
(B) Three
(C) Two
(D) One
(E) None

20. How many positive integers less than 1,500 do not have a 5 as any digit?
(A) 1,133
(B) 1,152
(C) 1,176
(D) 1,189
(E) 1,227

ST OP
If you finish before time is called, you may check your work on
this section only.
Do not turn to any other section in the test.

SECTION 3
Time — 25 minutes
24 Questions
(25-48)
Directions: For each question in this section, select the best answer from among the
choices given and fill in the corresponding circle on the answer sheet.

Each sentence below has one or two blanks, each blank indicating that something has
been omitted. Beneath the sentence are five words or sets of words labeled A through
E. Choose the word or set of words that, when inserted in the sentence, best fits the
meaning of the sentence as a whole.
Example:

Hoping to ------- the dispute, negotiators proposed a compromise that they felt would
be ------- to both labor and management.
(A) enforce . . useful
(B) end . . divisive
(C) overcome . . unattractive
(D) extend . . satisfactory
(E) resolve . . acceptable

25. Even though it claimed to always place the needs of the customer above all

25. Even though it claimed to always place the needs of the customer above all

else, the popular chain store lately has forgotten customer service in favor of

making money: it consistently ------- patrons while primarily focusing on -------.
(A) hordes . . losses
(B) shuns . . profits
(C) celebrates . . earnings
(D) upends . . savings
(E) neglects . . philanthropy
26. Basset hounds are always classified as -------, though not -------: they are slow to
get up from rest, but are always aware of their surroundings.
(A) energetic . . perceptive
(B) idle . . oblivious
(C) agreeable . . lazy
(D) shiftless . . conscious
(E) devout . . active
27. Always one to ------- excessively about his accomplishments, David was known
for his braggadocio and arrogance.
(A)

boast (B)

belittle (C)

verbalize (D)

minimize (E)

dwindle

28. 1970s cinema is often lauded for its -------: depicting undoubtedly realistic

situations, these films were a welcome respite from fantastical elements from
earlier eras.
(A)

verisimilitude (B)

euphemism

austerity (C)

implausibility (D)

chicanery (E)

29. Portraying the common field cricket’s movements as -------, the entomologist’s

29. Portraying the common field cricket’s movements as -------, the entomologist’s

research belied hundreds of years of assumptions that the field cricket was a ------ creature.

(A) tense . . hackneyed
(B) excitable . . vague
(C) ebullient . . vivacious
(D) spasmodic . . fitful
(E) kinetic . . placid

The passages below are followed by questions based on their content; questions

following a pair of related passages may also be based on the relationship between the

paired passages. Answer the questions on the basis of what is stated or implied in the
passage and in any introductory material that may be provided.
Questions 30-33 are based on the following passages.

30. This pair of passages considers which of the following?
(A) The inefficiency of current solar panels in absorbing bands of light
(B) The tendency of some brands of solar panels to overheat
(C) The faulty conductivity of silicon semiconductors
(D) The development of a solar panel that is more effective than current
models.

(E) The need for funding research to develop renewable energy
31. Atwater would most likely consider the last sentence in Passage 1 (lines 11-13)
to be

(A) an accurate claim
(B) a controversial statement
(C) a logical fallacy
(D) an exciting revelation
(E) a disputable finding
32. The tone of lines 24-27 (“Within … percent”) is best described as
(A) argumentative
(B) optimistic
(C) sarcastic
(D) nostalgic
(E) technical

33. Both passages mention the silicon in semiconductors to

33. Both passages mention the silicon in semiconductors to
(A) cite an example of a material that performs more efficiently than
expected

(B) present a type of device that physicists are still developing
(C) reference a material that is useful but limited
(D) identify the main fault with solar panels
(E) clarify a mistaken statement about infrared and ultraviolet light

Questions 34-42 are based on the following passage.
This passage, adapted from a 1995 short story set in Mexico, is about a girl named

Catalina who has left her small town and gone to university in Mexico City, the capital
city of Mexico.

34. The primary purpose of the passage is to describe
(A) Catalina’s unhappiness at her new school
(B) a formative encounter with a new friend
(C) an uncomfortable meeting between two students
(D) Catalina’s homesickness after leaving her small town
(E) Catalina’s relationship with Araceli at school

35. The first sentence of the passage (lines 1-3) suggests that the “girls in her

35. The first sentence of the passage (lines 1-3) suggests that the “girls in her
room” initially regarded Catalina as
(A) prudish
(B) ridiculous
(C) unattractive
(D) unhygienic
(E) alien
36. The action described in lines 5-6 (“she … homework”) exemplifies Araceli’s
(A) intelligence
(B) beauty
(C) hospitality
(D) condescension
(E) anger
37. Which of the following LEAST accurately characterizes Araceli as she is
represented in lines 3-14?
(A) Familiar
(B) Nurturing
(C) Stern
(D) Sympathetic
(E) Local

38. The primary purpose of Clara’s various questions in lines 22-36 is to

38. The primary purpose of Clara’s various questions in lines 22-36 is to
(A) encourage Catalina to join her at the protest
(B) interrogate Catalina about her childhood
(C) spark a political dialogue with Catalina
(D) force Catalina to change her political views
(E) test whether Catalina is able to protest
39. The author uses the image of the “key” (line 26) to convey the impression of
(A) a visual representation of protest
(B) opening things that had been hidden away
(C) an important political point
(D) a locked government building
(E) a protest song
40. The repetition of the word “really” in lines 37-39 serves to emphasize
Catalina’s

(A) consternation
(B) astonishment
(C) misanthropy
(D) befuddlement
(E) dishonesty

41. The fourth paragraph (lines 37-44) represents Catalina as

41. The fourth paragraph (lines 37-44) represents Catalina as
(A) hopeful
(B) suspicious
(C) deceptive
(D) apathetic
(E) thoughtful
42. The last paragraph (lines 45-50) suggests that, until she met Clara, Catalina
(A) believed that she would return to her village after graduation
(B) had no sympathy for the sufferings of local farmers
(C) did not have an intense interest in politics
(D) felt that the government represented her interests
(E) had decided not to go to political protests any more
Questions 43-48 are based on the following passage.
The following passage is from a 2011 article on the state of wild orchids throughout the
world.

43. The author refers to “aloe” (line 10) primarily to illustrate
(A) how Tanzania’s record of farming orchids has a historical precedent
(B) why farmers consider the models of scientists untrustworthy
(C) why some horticulturalists consider the trends in orchid farming
troubling

(D) why Tanzanian farmers are concerned about the state of orchids in their
region

(E) what Tanzanian farmers have done to increase their production of
orchids

44. In line 21, “outgrowth” most nearly means
(A) onset
(B) effect
(C) overharvest
(D) dearth
(E) parasite

45. The author supports the claim in lines 25-26 (“These … be”) by asserting that

45. The author supports the claim in lines 25-26 (“These … be”) by asserting that
farmers

(A) have avoided orchid extinction since 1983
(B) have favored the creation of national parks protecting orchids
(C) are occasionally required to move to find more orchid crops
(D) use orchid crops for things other than international flower sales
(E) have their own set of scientific data about global orchid crops
46. The author uses the statement in lines 29-31 (“And … it”) to emphasize that
(A) the main purchasers of orchids come from orchid-farming regions
(B) the extinction of aloe plants is not likely to be mirrored in orchid crops
(C) horticulturalists understand the cultural role of orchids better than
farmers do

(D) in certain areas, orchids have more than just an aesthetic value
(E) scientists who study orchids refuse to see the local importance of the
flowers

47. The passage suggests that all of the following are true of orchids EXCEPT
(A) they can be eaten and used in other food products
(B) they have been popular on international markets since the 1800s
(C) they grow in many of the same places as aloe crops
(D) there are legal restrictions on how they can be farmed and sold
(E) the health of the species is often assessed on an international level

48. The author indicates that “some Asian and African governments” (lines 45-46)

48. The author indicates that “some Asian and African governments” (lines 45-46)
do which of the following?

(A) Encourage aggressive farming techniques
(B) Restrict how much orchid material local populations can eat
(C) Employ orchid farmers to curate national parks
(D) Plan to take measures to protect orchid crops
(E) Boycott countries whose farmers harvest orchids illegally

ST OP
If you finish before time is called, you may check your work on
this section only.
Do not turn to any other section in the test.

SECTION 4
Time — 25 minutes
18 Questions
(21-38)
Directions: For this section, solve each problem and decide which is the best of the
choices given. Fill in the corresponding circle on the answer sheet. You may use any
available space for scratchwork.

Notes
1. The use of a calculator is permitted.
2. All numbers used are real numbers.
3. Figures that accompany problems in this test are intended to provide information
useful in solving the problems. They are drawn as accurately as possible

EXCEPT when it is stated in a specific problem that the figure is not drawn to
scale. All figures lie in a plane unless other wise indicated.

4. Unless otherwise specified, the domain of any function f is assumed to be the set
of all real numbers x for which f(x) is a real number.

Reference Information

The number of degrees of arc in a circle is 360.
The sum of the measures in degrees of the angles of a triangle is 180.

21. If c2 = 9, then c4 =

21. If c2 = 9, then c4 =
(A)

18

(B)

36

(C)

72

(D)

81

(E) 6,561

22. What is the average (arithmetic mean) of the first seven positive even
integers?

(A) 6
(B) 6.5
(C) 7
(D) 8
(E) 8.5

23. In the xy-coordinate system above,

is one side of an isosceles right triangle.

Which of the following coordinates could be a vertex of this triangle?
(A) (–4, 9)
(B) (2, 6)
(C) (6, 14)
(D) (8, 5)
(E) (8, 15)

24. What is the largest integer whose square root is less than 4 ?
(A)

9

(B) 12
(C) 15
(D) 16
(E) 25

25. In ΔRST above, RT = ST. What is the value of x ?
(A)

30

(B)

35

(C)

50

(D)

75

(E) 105

26. If there are s seconds in m minutes, what is s in terms of m ?
(A)
(B)
(C) 60 –2m
(D) m + 60
(E) 60m

27. The sum of x, y, and z is 14. If x, y, and z are positive integers such that x ³ y ³

27. The sum of x, y, and z is 14. If x, y, and z are positive integers such that x ³ y ³
z, what is the greatest possible value of z ?
(A) 3
(B) 4
(C) 5
(D) 6
(E) 12

For all integers a and b that are less than 5, 5a – b > ab.

28. Which of the following values for a and b show that the statement above is not
true?

(A) a = 5, b = 5
(B) a = 4, b = 6
(C) a = 3, b = 4
(D) a = 2, b = –3
(E) a = –4, b = 6

29. 200 people attended a concert for band Q. Band Q earned $15 for each person
who attended the concert and an additional $10 for each T-shirt sold. If 132

people bought one T-shirt each, how much, in dollars, did band Q earn from
the concert? (Disregard the $ sign when gridding your answer.)

30. If .5943 = (59.43)10–t what is the value of t ?

31. If

of m is 200 and

of n is 500, what is the value of n − m ?

32. In the figure above, ABCD and WXYZ are squares with areas 4 and 49,

respectively. DCXQ is a rectangle with area 16. What is the area of rectangle
PDQW ?

33. The table above shows the five flavors of ice cream cones sold at Krispy’s Cone
Parlor last week. If 480 Mint Chocolate Chip cones were sold last week, how
many Pistachio cones were sold last week?

34. In the figure above,

||

and

||

. What is the value of x ?

35. For a certain magic trick, Jen is asked to choose a number between 1 and 500.
If Jen chooses an even number that is divisible by both 3 and 23, what is one
possible number that Jen could have chosen?

36. If –2 ≤ a ≤ 3 and –4 ≤ b ≤ 2, what is the maximum value of

?

37. The total cost of 9 roses and 5 tulips is the same as the total cost of 6 roses and
9 tulips. The cost of each tulip is p times the cost of each rose. What is the
value of p ?

38. In the xy-plane, the line cx – dy = 2, where c and d are constants, intersects
the y-axis where y = –8. What is the value of d ?

ST OP
If you finish before time is called, you may check your work on
this section only.
Do not turn to any other section in the test.

SECTION 5
Time — 30 minutes
39 Questions
(1-39)
Directions: For each question in this section, select the best answer from among the
choices given and fill in the corresponding circle on the answer sheet.

The following sentences test correctness and effectiveness of expression. Part of each

sentence or the entire sentence is underlined; beneath each sentence are five ways of
phrasing the underlined material. Choice A repeats the original phrasing; the other

four choices are different. If you think the original phrasing produces a better sentence
than any of the alternatives, select choice A; if not, select one of the other choices.

In making your selection, follow the requirements of standard written English; that is,

pay attention to grammar, choice of words, sentence construction, and punctuation.
Your selection should result in the most effective sentence—clear and precise, without
awkwardness or ambiguity.
EXAMPLE:
Bobby Flay baked his first cake and he was thirteen years old then.
(A) and he was thirteen years old then
(B) when he was thirteen
(C) at age thirteen years old
(D) upon the reaching of thirteen years
(E) at the time when he was thirteen

1. In 1900, Wilbur Wright and his brother, West Side News publisher Orville

1. In 1900, Wilbur Wright and his brother, West Side News publisher Orville
Wright, journeyed to Kitty Hawk, North Carolina, they began their first
experiments with manned air gliders there.

(A) they began their first experiments with manned air gliders there
(B) it was where they began their first experiments with manned air gliders
(C) that was where they began their first experiments with manned air
gliders

(D) when the first experiments with manned air gliders were begun by them
(E) where they began their first experiments with manned air gliders
2. When Beethoven was thirteen years old, he has already begun composing
and publicly performing music; however, not until seventeen years later
would he write his first symphony.
(A) has already begun
(B) was already beginning
(C) is already to begin
(D) will already begin
(E) had already begun
3. The lead guitarist and the drummer fought constantly, and this caused the
guitarist starting his own new band.

(A) and this caused the guitarist starting
(B) so the guitarist started
(C) the guitarist was starting
(D) so as the guitarist was starting
(E) effecting in that the guitarist started

4. James Dean, having died shortly after the filming of Rebel Without a Cause, and

4. James Dean, having died shortly after the filming of Rebel Without a Cause, and
he was only able to receive an Academy Award for Best Actor posthumously.
(A) and he was only able to receive
(B) then he was only able to be receiving
(C) was only able to receive
(D) he was only able to receive
(E) therefore he was only able to receive
5. The school board, in enacting new anti-truancy laws that would discourage
students from cutting class and encourage regular school attendance.

(A) board, in enacting new anti-truancy laws that would discourage
students from

(B) board is enacting new anti-truancy laws, they will discourage students
(C) board enacted new anti-truancy laws that would discourage students
from

(D) board, which enacted new anti-truancy laws will discourage students
from

(E) board, who enacted new anti- truancy laws that will discourage students

6. Eugene Fama, a Nobel prize winner and one of the world’s most distinguished

6. Eugene Fama, a Nobel prize winner and one of the world’s most distinguished
American economists, is extolled by many as an authority on portfolio theory
and asset pricing.

(A) a Nobel prize winner and one of the world’s most distinguished
American economists, is extolled by many

(B) a Nobel prize winner and one of the world’s most distinguished
economists, and extolled by many

(C) being a Nobel prize winner and one of the world’s most distinguished
economists, and by many to be extolled

(D) he is a Nobel prize winner and one of the world’s most distinguished
economists, many extolling him

(E) as a Nobel prize winner and one of the world’s most distinguished
economists, and by many to be extolled as

7. The Willis (formerly Sears) Tower, with its 108 stories and 1,451 feet, are
easily considered Chicago’s most famous landmark.
(A) are easily considered
(B) easily considered
(C) which are easily considered
(D) given easy consideration as
(E) is easily considered

8. Pollsters canvassing public opinion are discovering that most voters want

8. Pollsters canvassing public opinion are discovering that most voters want
improved economic conditions, better health care, and have more social
services programs for the elderly.

(A) have more social services programs for the elderly
(B) with more social services programs for the elderly
(C) to have more social services programs for the elderly
(D) more social services programs for the elderly
(E) having more social services programs for the elderly
9. The strategy board game Chinese checkers, an easy game to learn, it allows
players only single-step moves or moves in which pieces jump over other

pieces, and the basic goal is simply to reach the other side of the board before
any opponents do the same.

(A) checkers, an easy game to learn,
(B) checkers is an easy game to learn,
(C) checkers is an easy game to learn because
(D) checkers, an easy game to learn because
(E) checkers, an easy game to learn in that
10. The teacher explained that copying or by otherwise using another student’s
work to solve the problem was considered cheating.
(A) or by otherwise using
(B) or otherwise using
(C) or otherwise used
(D) or to otherwise use
(E) or if otherwise used

11. NASA astronauts, before going into space, are required to accumulate a

11. NASA astronauts, before going into space, are required to accumulate a

number of flight hours in military jets in order to become a pilot certified to
fly the space shuttle.

(A) to accumulate a number of flight hours in military jets in order to
become a pilot

(B) to accumulate a number of flight hours in military jets, they thus
become pilots

(C) they will accumulate a number of flight hours in military jets, thus
becoming a pilot

(D) that they accumulate a number of flight hours in military jets in order
to become a pilot

(E) to accumulate a number of flight hours in military jets in order to
become pilots

12. The critic claimed that the paintings from Picasso’s Blue Period were more

representative of early twentieth-century modern art than other artists who
painted during his time.

(A) other artists who painted during his time
(B) those artists from the same time in art history
(C) artists of his time
(D) those of any other artists of his time
(E) the same time in modern art

13. While learning to ride the new bicycle, a pink one with green tassels and a

13. While learning to ride the new bicycle, a pink one with green tassels and a

banana seat, a dog ran in front of Rebekah and caused her to swerve into a
fire hydrant.

(A) While learning to ride the new bicycle, a pink one with green tassels
and a banana seat, a dog ran in front of Rebekah and caused her to
swerve into a fire hydrant.

(B) A dog ran in front and caused Rebekah’s swerve into a fire hydrant

while learning to ride the new bicycle, a pink one with green tassels
and a banana seat.

(C) A dog ran out while learning to ride the new bicycle, a pink one with

green tassels and a banana seat, and it caused Rebekah to swerve into a
fire hydrant.

(D) While learning to ride the new bicycle, a pink one with green tassels
and a banana seat, a fire hydrant was run into by Rebekah when she
swerved to avoid a dog.

(E) While Rebekah was learning to ride the new bicycle, a pink one with

green tassels and a banana seat, a dog ran in front of her and caused her
to swerve into a fire hydrant.

14. Daily exercise involving cardiovascular activities are proven to reduce the risk
of conditions such as diabetes and high blood pressure.
(A) are proven to reduce
(B) have been proven to reduce
(C) has been proven as reducing
(D) has been proven to reduce
(E) prove that they reduce

15. It possessed the most advanced safety features available in its time, and it was

15. It possessed the most advanced safety features available in its time, and it was
generally considered unsinkable, the RMS Titanic sank along with 1,500 of its
passengers on April 15, 1912.

(A) It possessed the most advanced safety features available in its time, and
(B) During its time, it possessed the most advanced safety features
available, and

(C) Although it possessed the most advanced safety features available in its
time and

(D) Despite it possessing the most advanced safety features available during
its time,

(E) It possessed the most advanced safety features available in its time,
although

16. Each year hundreds of bicyclists from around the world pack up their

belongings, travel to France to participate in the Tour de France bicycle race.
(A) to France to participate in the Tour de France bicycle race
(B) and in France they participate in the Tour de France bicycle race
(C) to France, participating in the Tour de France bicycle race
(D) to France, and the Tour de France bicycle race is participated in
(E) to France, and participate in the Tour de France bicycle race

17. If more travelers were to check their bags rather than bring carry-ons, the lines
through airport security would be much shorter than they currently are.
(A) were to check their bags rather than bring carry-ons
(B) were to check their bags rather than instead take carry-ons
(C) will check their bags rather than instead taking carry-ons
(D) check their bags rather than bring carry-ons
(E) check their bags but rather instead bring carry-ons
18. Jana must move her belongings to the new apartment today regardless of

18. Jana must move her belongings to the new apartment today regardless of
whether she will be able to unpack them promptly when she arrives.

(A) of whether she will be able to unpack them promptly when she arrives
(B) of if she can unpack it promptly upon arrival
(C) of whether or not she will be able to unpack it promptly upon arriving
(D) of if she could unpack them immediately upon arrival
(E) of whether she can unpack it promptly when she arrives
19. Famous for founding the world’s first private detective agency, another fact

about Eugène Vidocq is that before he became a detective, he was a criminal
and an army deserter.

(A) another fact about Eugène Vidocq is that before he became a detective,
he was a criminal and an army deserter

(B) before becoming a detective he was a criminal and an army deserter is
another fact about Eugène Vidocq

(C) Eugène Vidocq’s career before he became a detective was that of a
criminal and an army deserter

(D) another fact about Eugène Vidocq is that before he became a detective,
he was a criminal and an army deserter

(E) Eugène Vidocq was a criminal and an army deserter before he became a
detective

20. The reigns of Atilla the Hun, like many other early rulers of the Hun tribes,
were marked by bloody conquests and ceaseless wars.

(A) Hun, like many other early rulers of the Hun tribes, were
(B) Hun and many other early rulers of the Hun tribes were
(C) Hun, like those of many other early rulers of the Hun tribes, was
(D) Hun and many other early rulers of the Hun tribes was
(E) Hun, like those of many other early rulers of the Hun tribes, had been

The following sentences test your ability to recognize grammar and usage errors. Each

sentence contains either a single error or no error at all. No sentence contains more
than one error. The error, if there is one, is underlined and lettered. If the sentence
contains an error, select the one underlined part that must be changed to make the

sentence correct. If the sentence is correct, select choice E. In choosing answers, follow
the requirements of standard written English.
EXAMPLE:

21.

22.

23.

23.

24.

25.

26.

27.

27.

28.

29.

30.

31.

31.

32.

33.

34.

Directions: The following passage is an early draft of an essay. Some parts of the
passage need to be rewritten.

Read the passage and select the best answers for the questions that follow. Some

questions are about particular sentences or parts of sentences and ask you to improve
sentence structure or word choice. Other questions ask you to consider organization

and development. In choosing answers, follow the requirements of standard written
English.

Questions 35-39 are based on the following passage.
(1) Many think that spending hours studying vocabulary flashcards and books

on grammar are the best way to learn a foreign language. (2) Most linguists,

however, would also suggest interacting with native speakers. (3) Doing so helps

one improve one’s accent and forces one to practice speaking as well as listening.
(4) When individuals practice speaking in foreign language, they strengthen

muscles that they do not use when speaking in their own tongue and therefore
become better speakers in the new language.

(5) Dedicating regular time to study is also essential to learning a new language,

according to many experts. (6) The fact of being irregular in your studies, they
find, is the worst action you can take if you want to become fluent in a new

language. (7) In other words, when you study regularly, whether you study for two
hours per day or for thirty minutes per day, you are exercising your new skills and

preventing yourself from forgetting what you have learned. (8) Practice is essential
for improving other skills, such as playing an instrument, too.

(9) Learning a new language sometimes requires you to make a fool of yourself.

(10) For a language learning process to be effective, you must practice new skills

in settings that include others. (11) When individuals practice their language skills
by interacting with native speakers, they are literally going back to being two

year-olds, and are likely to make mistakes. (12) And during a conversation, when
speech is impromptu, they are more likely to occur than during planned
presentations or in essays.

35. Which of the following is the best revision of the underlined part of sentence 1

35. Which of the following is the best revision of the underlined part of sentence 1
(reproduced below)?

Many think that spending hours studying vocabulary flashcards and books on
grammar are the best way to learn a foreign language.
(A) (as it is now)
(B) spending hours studying vocabulary flashcards and books on grammar
is

(C) the hours they spent studying vocabulary flashcards and books on
grammar were

(D) if you spend hours studying vocabulary flashcards and books on
grammar, that is

(E) after spending hours studying vocabulary flashcards and books on
grammar one will have discovered

36. In context, which of the following is the best version of the underlined part of
sentence 6 (reproduced below)?

The fact of being irregular in your studies, they find, is the worst action you can
take if you want to become fluent in a new language.
(A) (as it is now)
(B) Such irregularity
(C) Being irregular like that
(D) Studying irregularly
(E) To be so irregular

37. In context, which of the following is the best revision of the underlined part of

37. In context, which of the following is the best revision of the underlined part of
sentence 11 (reproduced below)?

When individuals practice their language skills by interacting with native speakers,
they are literally going back to being two year-olds, and are likely to make
mistakes.

(A) (as it is now)
(B) are despite this
(C) are, in contrast,
(D) are, for example,
(E) are, as it were,
38. In context, the pronoun “they” in sentence 12 refers to which of the following?
(A) Individuals who study foreign languages
(B) Conversations between those who study a foreign language and native
speakers of that language

(C) New skills gained by practicing conversation in a foreign language
(D) Conversational mistakes made by foreign language students
(E) Settings that include both native and non-native speakers of a language
39. Which of the following is unnecessary and should be deleted from the passage?
(A) Sentence 3
(B) Sentence 4
(C) Sentence 7
(D) Sentence 8
(E) Sentence 11

ST OP

If you finish before time is called, you may check your work on
this section only.
Do not turn to any other section in the test.

PRACTICE TEST 3 ANSWERS

You will find a detailed explanation for each question beginning on
this page.

SCORING YOUR PRACTICE PSAT
Critical Reading
After you have checked your answers against the answer key, you
can calculate your score. For the two Critical Reading sections
(Sections 1 and 3), add up the number of correct answers and the
number of incorrect answers. Enter these numbers on the worksheet
on the next page. Multiply the number of incorrect answers by .25
and subtract this result from the number of correct answers. Then
round this to the nearest whole number. This is your Critical
Reading “raw score.” Next, use the conversion table to convert your
raw score to a scaled score.

Math
Calculating your Math score is a bit trickier, because some of the
questions have five answer choices (for these, the incorrect answer
deduction is .25), and some are Grid-Ins (which have no deduction
for wrong answers).
First, check your answers to all of the problem-solving questions on
Sections 2 and 4. For Section 2 and questions 21–28 of Section 4,
enter the number of correct answers and the number of incorrect
answers into the worksheet on the next page. Multiply the number of
incorrect answers by .25 and subtract this result from the number of
correct answers. For questions 29–38 of Section 4, the Grid-In
questions, simply enter the number of correct answers. Now, add up
the totals for both types of math questions to give you your total
Math raw score. Then you can use the conversion table to find your
scaled score.

Writing Skills
The Writing Skills section should be scored just like the Critical
Reading sections. Add up the number of correct answers and the
number of incorrect answers from Section 5, and enter these
numbers on the worksheet on the next page. Multiply the number of
incorrect answers by .25 and subtract this result from the number of
correct answers. Then round this to the nearest whole number. This
is your Writing Skills raw score. Next, use the conversion table to
convert your raw scores to scaled scores.

WORKSHEET FOR CALCULATING YOUR
SCORE

SCORE CONVERSION TABLE

Chapter 10
Practice Test 3: Answers and
Explanations

Section 1
1. C Start with the second blank. Since the restaurant was rarely
crowded due to the wait staff, replace the blank with a
negative word such as “rude” or “disrespectful.” Eliminate
everything except choices (B) and (C). Now move to the
first blank and notice the trigger word but, which indicates
that even though the wait staff was negative, the cuisine
must be positive. Eliminate choice (B) since unremarkable is
not a positive word. Choice (C) is the correct answer.
2. D Start with the second blank. Since the sentence states that
food production will be altered due to what’s happening to
the honeybee, the honeybee must be important to food
production, so replace the second blank with “important.”
Eliminate choices (A), (B), and (E). Since the honeybees
have an effect on food production, replace the first blank
with a word that indicates a change in the population, such
as “increase” or “decrease.” Eliminate choice (C) since
renouncing doesn’t fit either of those words. Choice (D) is
the correct answer.
3. A The sentence states that the Leaning Tower of Pisa … is
regarded as one of the most remarkable buildings in the world,
but this statement is preceded by the trigger word although.
Therefore the blank should be replaced with something that
means “unremarkable” or “inferior.” Eliminate choices (B)
and (C) since they are the opposite of the clue, and also
choice (E) because it isn’t a negative. Choice (D) is too
strong since repugnant means “very ugly or distasteful.”
Choice (A) is the correct answer.
4. B Start with the second blank. The second part of this
sentence mentions that players hit each other with careless

abandon and that no one was interested in a particular type
of play. Therefore, the second blank should be the opposite
of careless, so choose a word that means “careful.” Eliminate
choices (C) and (D). Because of the semicolon, which is a
same-direction trigger, the first part of the sentence must
agree with the second. Fill in the first blank with something
such as “not caring” or “not knowing.” Eliminate choices
(A) and (E). Choice (B) is the correct answer.
5. A The sentence contrasts the Photorealistic style and the
Expressionist style. In contrast to the Expressionist painter,
who uses color to create an emotional impact, the
Photorealistic painter would “try” to copy every detail. The
missing word must mean “try.” Endeavor means “attempt,”
making choice (A) the correct answer.
6. B Start with the second blank. The sentence states that the
physics instructor wanted a victory and did something with
the work of her honors physics class. Since a victory was
needed, replace the second blank with “display” or “used.”
Eliminate everything but choices (B) and (C). If the teacher
only used the best work, she must have wanted to
“guarantee” a victory. Use that word for the first blank and
eliminate choice (C) since it’s the opposite of “guarantee.”
Choice (B) is the correct answer.
7. E The sentence states that the explorer’s recent
exploits … confirmed that he had no intention of worrying
about his own safety, so the trigger word but should indicate
that the exploits were the opposite of safe, so replace the
blank with “danger.” Choice (E) is the correct answer.
8. D The blank in this question must match the clues, which are
mean-spiritedly mocked and taunted, so recycle a word from
the sentence and replace the blank with “mean-spirited.”
Choice (D) is the only choice that has a negative meaning,

and it means “causing harm” or “evil/wicked,” so choice
(D) is the correct answer.
9. C The correct answer to this question must be stated directly
in the passage, so go to the answer choices and eliminate
anything that cannot be proven. Choice (A) is too extreme,
so eliminate it. Choice (B) doesn’t work since nothing is
said about most readers. Choice (C) could work since the
first line states that the Naturalist movement was the
“natural result of Romanticism and Surrealism.” Choice (D)
seems okay at first, but the passage only states that Crane’s
is as example of Naturalism, not that it was the first
Naturalist novel. Choice (E) uses the wrong meaning of the
word environment. Choice (C) is the correct answer.
10. E The author uses Maggie’s suicide as an example of
something found in a Naturalist novel. Choice (A) doesn’t
work because the passage never explicitly states that
Maggie’s home life was unsatisfying. There is no evidence
that Maggie’s story wouldn’t be told in a Surrealist novel, so
eliminate choice (B). Eliminate choice (C) since this is only
one example of a Naturalist novel. Choice (D) is wrong
since the passage is not focused on the Romantic
movement. Choice (E) fits since the passage states that, in
the Naturalist movement, one’s environment played a much
more pivotal role in determining one’s destiny than choice and
action, so it is the correct answer.
11. B The first sentence states that The advent of social media sites
such as Facebook and Twitter has had a dichotomous effect on
the landscape, so look for an answer that says something
about having conflicting or different effects on the world.
Eliminate choices (A) and (C) since this passage is neutral,
and there is no evidence to support bemoan or criticize.
Choice (D) is also out since celebrate is positive. Choice (B)
fits since it says differing consequences. Eliminate choice (E)

since our daily lives is irrelevant. Choice (B) is the correct
answer.
12. C Since this passage states that Twitter has also been responsible
for a complete overhaul in government in Iran, the use of not
ironically indicates that stating Twitter played this role is
serious and not meant as a joke. Eliminate (A) since
impossible is too extreme. Eliminate choice (B) because there
is no mention of anyone having a flippant attitude. Choice
(C) could work since it states Twitter’s role was integral,
which matches complete overhaul. Eliminate choice (D)
because the passage does not make such a comparison.
Eliminate choice (E) since the author isn’t trying to cast
doubt on anyone. Choice (C) is the correct answer.
13. A The full lines read as follows: In a span of only thirty years,
the number of children who play musical instruments has been
cut in half. The word only indicates the quickness with
which this transformation has occurred, lending support to
choice (A). The author goes on to list the troubling aspects
of this trend, so none of the other choices work in this
context.
14. B The author of Passage 1 discusses the survey in the first part
of the second paragraph: Music in Peril is not the collection
of urban legends that most of its critics will accuse it of being. It
is a set of data collected from elementary and middle schools all
over the country. With schools represented from each of the 50
states, it accounts for all the great diversity in this country.
From this statement, it can be inferred that the author
disapproves of urban legends and approves of data collected
from all over the country that accounts for all the great
diversity in this country. The author is most concerned with
span and diversity, as choice (B) suggests. While choice (D)
does partially describe Music in Peril’s data, it does not
account for all the data, so it can be eliminated. Choice (E)

addresses the issue of race, but not the other types of
diversity described in the passage.
15. C The author of Passage 2 does not dispute the methods
employed by the statisticians described in Passage 1. She
instead thinks the criteria should be changed. As she writes
in the last paragraph, The survey can’t capture the fact that
classical music is not the only place to find interesting, complex
music anymore, except by the most conservative, crustiest
definitions. In this sense, the author of Passage 2 would
likely consider the diversity of the groups surveyed
irrelevant because the survey is based on faulty premises, as
suggested in choice (C). The author of Passage 2 does not
take issue with Passage 1’s data but more with its premises
and conclusions.
16. D The main point of the final paragraph of Passage 1 comes
through in the last two sentences: True musical proficiency is
the result of many years of encouraging musical education, and
not only for those who eventually become musicians. Ours is a
dire world indeed when not only have our musicians lost the
ability to play but also the broader populace has lost the
discernment and ability to hear them. In other words, musical
education does not only affect schoolchildren but affects
society as a whole, as choice (D) paraphrases. While choice
(B) may be implied in the passage, it is never directly
stated, so this answer choice has to be eliminated.
17. A The author of Passage 2 refers to Passage 1’s conclusions as
apocalyptic and evidence that all the bad things we suspect are
worse than we even knew. Passage 2’s sarcastic, dismissive
language suggests that the author thinks Passage 1’s
conclusions are a bit dramatic, or overstated, as choice (A)
suggests. Although she disagrees with these conclusions, she
does not refer to the author of Passage 1 as dishonest,
merely misguided, eliminating choice (E).

18. D The author of Passage 2 refers to these apocalyptic surveys as
providing evidence that all the bad things we suspect are worse
than we even knew. The survey in the answer choices must
therefore describe a negative trend, eliminating choices (B),
(C), and (E). Choice (A) describes a trend, but it is one that
is simply true. It does not contain within it the value
judgment that choice (D) does. Only choice (D) remains, as
exactly the kind of apocalyptic survey she considers
commonplace.
19. C The third paragraph of Passage 2 states the following: Music
programs have been slashed at many public schools, and less
than half as many children today are learning instruments than
were the generations of forty or fifty years earlier. And this
statistical certainty is not limited to the less fortunate areas of
the country. Words like many and limited refer to the range of
the problem, as choice (C) suggests. The author of Passage 2
does accuse Music in Peril of both conservatism and bias, but
in these lines, she is conceding that the study describes a
wide-ranging trend, eliminating choices (D) and (E).
20. E The word landscape is used in the beginning of the fourth
paragraph: The musical landscape is changing, yes, but not in
the distressing way that Music in Peril wants to suggest. The
survey can’t capture the fact that classical music is not the only
place to find interesting, complex music anymore. In other
words, the typical definition suggests that classical music is
the only interesting, complex type of music—a claim that the
author disputes, lending support to choice (E). Choice (D) is
correct to say shifting, but the trend is not impossible to
describe, as the author tries to describe it.
21. D Throughout the fourth paragraph, the author uses terms like
most conservative, traditional, musical categories that don’t
apply anymore, institutions of old, and irrelevant. In other
words, the categories are still being used even though they

have not changed to reflect current realities and are
therefore inflexible, as choice (D) suggests. Other terms may
provide alternate meanings for the slangy word crusty, but
they do not apply here.
22. A The last sentence of Passage 2 says the following: All that is
really happening is that the institutions of old are trying to hold
on for dear life and actually belong in the same irrelevant pile
as studies on the decline of cursive or telephone conversations.
The key word here is irrelevant, and the author of Passage 1
would likely respond by noting the larger relevance of the
project, as choice (A) does. There is no support in Passage 1
for choices (B), (C), and (E). Choice (D) may be true, but it
would not respond to Passage 2’s criticism.
23. E Compare the first sentences of both passages. Passage 1
states, Music in Peril confirms most of our worst suspicions,
suggesting a concerned or saddened tone. Passage 2 states,
Music in Peril is hardly surprising in our era of apocalyptic
surveys, yet more evidence that all the bad things we suspect are
worse than we even knew, which is far more sarcastic and
dismissive. Choice (A) is correct only for Passage 1, and
choice (D) is correct only for Passage 2. The only choice
that correctly identifies the tone in each of the passages is
choice (E).
24. B Passage 2 is primarily a critique of the ideas in Passage 1,
which eliminates choices (C) and (D). Passage 2 does not,
however, provide new findings or new data, which
eliminates choices (A) and (E). Only choice (B) remains,
and it correctly identifies Passage 2’s issue with the
premises of Passage 1’s argument, namely that classical
music is the main outlet for interesting, important music.

Section 2
1. C Start by writing out the equation and plugging in the given
information. Since st = 6, the equation becomes 2r(6) =
60. Multiply the 2 and the 6 on the left side to get 12r =
60. It is possible to Plug In The Answers (PITA) at this
point, but it is quicker to simply divide each side of the
equation by 12. Therefore, r = 5 and (C) is the credited
response.
2. C This is a Plugging In question for which the number to plug
in is provided. Start by plugging x = 4 into the two
expressions. (x + 5)2 becomes (4 + 5)2, which is (9)2 or
81.
becomes
, which is
or 3. “Difference”
means subtraction, so subtract 3 from 81 to get 78. Choice
(C) is the credited response.
3. E The question only asks about a number in the overlap
between sets E and F, so the correct answer cannot be in set
N. Therefore, (A) and (B) can be eliminated, as those are
negative numbers. Check each remaining answer choice to
determine if it is in set E and set F. The numbers in (C) and
(D) are not even, so those can be eliminated. The number in
(E) is even, and it is a multiple of 5, so (E) is the credited
response.
4. D This is a Plugging In question in which the values for the
variable are provided. Start with case I and plug in n = 4.
This yields 3(4) = 12, which is true. Now plug in n = 5.
3(5) is 15, which is not equal to 12. Since the equation is
not satisfied by both values of n, case I is false. Therefore,
(A), (C), and (E) can be eliminated. Choices (B) and (D)
both contain case III, so it must be true and does not need

to be tested. Only case II needs to be evaluated to determine
whether (B) or (D) is the credited response. Plug n = 4 into
case II, which yields (4)2 – 9(4) + 20 = 0. This becomes 16
– 36 + 20 = 0, or –20 + 20 = 0. This is true, so test n =
5. The equation becomes (5)2 – 9(5) + 20 = 0, which
equals 25 – 45 + 20 = 0 or –20 + 20 = 0. This is also
true, so both cases II and III are true, and (D) is the credited
response.
5. B If the shape in the figure is a semicircle, then the line across
the bottom is the diameter and a straight line. There are
180° in a straight line, so 60 + a + a + a + a + a = 180.
This simplifies to 60 + 5a = 180. From here, the equation
can be solved for a. PITA will work as well, since the
question asks for a specific amount. If a = 30, the value in
(C), the equation is 60 + 5(30) = 180. This becomes 60 +
150 = 180, or 210 = 180. This is not true, so (C) can be
eliminated. That value for a was too large, so (D) and (E)
can be eliminated as well. Try the value in (B), a = 24, and
the equation is 60 + 5(24) = 180, or 60 + 120 = 180.
This is true, so (B) is the credited response.
6. B Isosceles right triangles have two equal legs. The angles of
isosceles right triangles are 45°, 45°, and 90°. It is one of the
special right triangles, so the sides have a predictable
relationship of x:x: x . If the leg is x, then the hypotenuse
is x . In this triangle, the leg is 6 , so the hypotenuse,
which is y, is 6. Therefore, (B) is the credited response.
Knowing the special right triangles saves time on the test,
but it is not necessary to solve this problem. If both legs are
equal to 6, the Pythagorean Theorem states that 62 + 62 =
y2. This can also be used to solve for y.
7. A First, determine what percent of the students typically spent

3 hours or more doing homework each night. The percents
must add up to 100, so 5 + 10 + 63 + 15 + p = 100.
This simplifies to 93 + p = 100, so p = 7%. Now find 7%
of the total number of students. Translating the English to
math, 7% means 7 out of 100, “of” means to multiply, and
the total number of students equals 800. The number of
students who spent 3 hours or more equals

× 800 =

56, so (A) is the credited response.
8. D When asked for a specific value and given numbers in the
answer choices, PITA. Start with (C) and plug in 4 for x.
The inequality becomes 2 < 2(4) – 6 < 4, or 2 < 8 – 6 <
4. This becomes 2 < 2 < 4, which is not true, so (C) can be
eliminated. A larger value is needed for x to make the
inequality true, so (A) and (B) can also be eliminated. Only
choices (D) and (E) remain, and the value in (E) is easier to
plug in. If x = 5, the inequality becomes 2 < 2(5) – 6 < 4.
This simplifies to 2 < 10 – 6 < 4, or 2 < 4 < 4. This is
also not true, so (E) can be eliminated, and (D) is the
credited response.
9. B When asked for a specific value and given numbers in the
answer choices, PITA. Start with the value in (C), which is
9. If x = 9, the radius of the semicircle is 9. The area of the
semicircle is

πr2 or

π(9)2. This equals

π(81), which is

40.5π. The question states that the area of the semicircle is

18π, so (C) can be eliminated. This value is too large, so (D)
and (E) can be eliminated as well. For (B), if x = 6, the
radius is 6 and the area is

π(6)2 or

π(36). This equals

18π, so (B) is the credited response.
10. A When asked for a specific value and given numbers in the
answer choices, PITA. This question asks for the least value
that will work, so start with the value in (A). If 11 pennies
are transferred from jar L to jar N, jar L will have 185
pennies in it and jar N will have 186 pennies in it. Since jar
M has only 184 pennies in it, jar N has more pennies than
each of the other two jars. Therefore, (A) is the credited
response.
11. D This is a pattern question, and the fact that the sequences
“continue indefinitely” makes it sound like it will be a lot of
work. The best approach is to simply start writing the
sequences out until a pattern emerges, which it is likely to
do fairly quickly. The sequence in the left column will be: 0,
7, 14, 21, 28, 35, 42, 49, 56, 63, etc. The sequence in the
right column will be 12, 16, 20, 24, 28, 32, 36, 40, 44, 48,
etc. At this point, both sequences contain the number 28 as
the 5th term, so there is at least one row in which the terms
are equal. Therefore, (E) can be eliminated. From the 6th
term on, the number in the sequence in the left column is
larger than the corresponding number in the right column.
The sequence on the left will continue to increase faster
than the one on the right, so the two sequences will never
have equal numbers in any row again. There was only one
match, so (D) is the credited response.
12. D With variables in the answer choices, Plug In. If the

woman’s ride to the airport is 10 miles, m = 10. Her total
fare would be $2.50 for the one-time charge and $3 for
each of the 10 miles travelled, or 2.50 + 3(10), which is
$32.50. Now, to find the cost “per mile,” divide the fare of
$32.50 by the number of miles, which equals 10. This
results in $3.25, which is the target answer. Now plug m =
10 into the answer choices to see which one equals $3.25.
Choice (A) becomes 10 + 2.50, which equals 12.50. This is
not the target answer, so (A) can be eliminated. Choice (B)
becomes 2.50 + 3(10), which equals 32.50. This is the total
fare, not the fare per mile, so (B) is a trap answer and can
be eliminated. Choice (C) becomes 2.50(10) + 3(10),
which is much too large and can be eliminated without
even calculating. Choice (D) becomes
equals

, which

or $3.25. This is the target answer, but all 5

answer choices must be checked when Plugging In, in case
more than one results in the target answer. Choice (E)
becomes

, which equals

or $2.80. This is not

the target answer, so (D) is the credited response.
13. A When dealing with graphs of functions, f(x) or g(x) is the y
value for any given x. The question asks which graph has

exactly one value of x that makes g(x) = 0, so draw a line
on each graph in the answer choices at y = 0. This is also
the x-axis of the xy-coordinate plane in each graph. The
number of points of intersection between the graph of g(x)
and the line drawn will be the number of values for which x
makes g(x) = 0. For (A), the graph will look like the
following:

There is only one point of intersection between the graph
and the line y = 0, at the circled point. If the same steps
are followed with (B), there are two points of intersection.
For (C), there are four, and (D) and (E) each have three
points of intersection. Therefore, (A) is the credited
response.
14. E For geometry questions that do not have a figure, draw one.
If one side of the rectangular solid is a square, the opposite
side must also be a square. Draw the other 4 sides as
rectangles that are not square, if possible. This will
determine what the greatest number of “not square” sides
can be. The rectangular solid could look something like the
following:

The front and back are squares, but the other four sides are
not square. Therefore, (E) is the credited response.
15. E When dealing with functions, the value in parentheses is the
x value, and f(x) or p(x) is the value that comes out of the
function when that x value is put in. To find the value of
p(4), look up where x = 4 on the chart and find the
corresponding p(x) value. According to the chart, p(4) = 7.
Now find where x = 2 to determine that p(2) = 3. Plug
these values into the equation 3p(4) + p(2) to get 3(7) + 3
= 21 + 3 = 24. Therefore, (E) is the credited response.
16. C Probability is defined as the number of outcomes that fulfill
the requirements divided by the total number of possible
outcomes. The total number of possible outcomes consists
of the 4 options from the board on the left multiplied by the
8 options from the board on the right. This yields 32 total
possible outcomes. Now, to determine how many scores are
at least 10, the best method is to start listing them out. Be
systematic so that none get overlooked. If the number on
the board on the left is 4, the numbers from the board on

the right that will result in a score of at least 10 are 8, 7,
and 6. If the number of the left is 3, the numbers on the
right that will result in a score of at least 10 are 8 and 7. If
the number on the left is 2, the number on the right must
be 8. There are no other combinations that will have a sum
of 10 or more, so there are 6 outcomes that fulfill the
requirements. Therefore, the probability is
reduces to

, which

. Choice (C) is the credited response.

17. D When asked for a specific value and given numbers in the
answer choices, PITA. Start with the middle choice, (C) and
assume that z = 90°. If it does, the angle opposite z will
also be 90°. This leaves 180° out of the total 360˚ in the
circle for the shaded regions. This 180˚ is divided equally
between the two shaded regions, so each of those is 90° as
well. Now check these values with the information given in
the problem to see if they work. The average of the
unshaded regions is

, which equals 90, and the sum

of the shaded regions is 90 + 90, which equals 180. These
two values are not equal, so (C) can be eliminated. The sum
of the shaded regions was too large, so to make those

smaller, a larger value is needed for z in the unshaded
regions. Therefore, (A) and (B) can be eliminated as well.
For (D), if z and the angle opposite z each equal 120°, they
add to 240°. There are 120˚ left for the shaded regions, so
each of those equals 60°. Now the average of the unshaded
regions is

, which equals 120, and the sum of the

shaded regions is 60 + 60, which equals 120. These two
results are equal, so (D) is the credited response.
18. C For questions with unknown variables, Plug In for those
variables, following any restrictions set forth in the
question. In this case, when the three numbers are
multiplied together, the result is a negative number. This
means that either one of the numbers is negative and two
are positive, or all three are negative. Start with the first
situation and pick a negative integer for f, since it is less
than the other two numbers, and positive integers for g and
h. If f = –2, g = 3, and h = 4, fgh = –24. This fits the
requirements, so these numbers work. For these values,
cases I and II are true, but case III is false. Therefore, (D)
and (E) can be eliminated, as those contain case III. Now try
other values for the variables, making all three of them
negative. If f = –5, g = –3, and h = –1, fgh = –15. These
values still fit the requirements and cases I and II are still
true. Try a few more combinations of numbers, just to be
certain that cases I and II are always true. Since they are,
(C) is the credited response.
19. C When given a geometry question with no figure, draw one.
Start with points M and N.

Now draw a point that could be 6 units from M and 2 units
from N. It could look like the following:

Another point could be below line
position, like this

in the same

There are no other points that can be drawn that are 6 units
away from M and 2 units away from N, so (C) is the
credited response.
20. A The numbers in these answer choices are very large. Rather
than count the number of integers that do not have 5 as any
digit, count the number that do and subtract them from the
total number of integers less than 1,500. This will still be a
lot of integers, so start by listing out those with a 5 in them
until a pattern emerges. Between 1 and 99, the integers that
contain a 5 as any digit are 5, 15, 25, 35, 45, 50, 51, 52, 53,
54, 55, 56, 57, 58, 59, 65, 75, 85, and 95, for a total of 19
integers. For the numbers 100-199, there will again be 19
integers with a 5 as a digit. The same is true for 200-299,
300-399 and 400-499. For the numbers between 500 and
599, every one of them will contain at least one 5 as a digit,
so that adds 100 more to the list. There will be 19 more
integers added to the list from each of the following sets of
100: 600-699, 700-799, 800-899, 900-999, 1,000-1,099,
1,100-1,199, 1,200-1,299, 1,300-1,399, and 1,400-1,499. In
total, the number of integers with a 5 as any digit will

include the 100 from 500 to 599 and the 19 from each of
the other 14 sets of 100 listed above. Therefore, Total =
100 + 19(14) = 100 + 266 = 366. Now subtract 366
from the total number of integers less than 1,500, which is
1,499, to get 1,499 – 366 = 1,133. Choice (A) is the
credited response.

Section 3
25. B Start with the second blank. The sentence states that the
popular chain store lately has forgotten customer service in
favor of making money, so replace the second blank with
“money.” Eliminate everything except choices (B) and (C).
Since the first part of the clue states that the chain store has
forgotten customer service, replace the first blank with
“forgets.” Eliminate choice (C). Choice (B) is the correct
answer.
26. B Start with the first blank. The sentence says that basset
hounds are slow to get up from rest, but are always aware of
their surroundings. Replace the first blank with “slow” and
eliminate everything except choices (B) and (D). Replace
the second blank with “unaware.” Eliminate choice (D).
Choice (B) is the correct answer.
27. A David is described in this sentence as being known for his
braggadocio and arrogance, so replace the first blank with
“brag.” Choice (A) is a good fit. Choice (C) might work, but
verbalize only means to talk, so there is no hint of
braggadocio and arrogance. Choice (A) is the correct answer.
28. A The sentence states that 1970s cinema is celebrated for
depicting undoubtedly realistic situations, in contrast to the
fantastical elements from earlier eras, so replace the blank
with “honest.” Choice (A) is a good fit. Choice (B) means
“serious,” which doesn’t match “honest” as well as choice
(A) does. Eliminate choices (C) and (D) since both are the
opposite of “honest” and choice (E) since it doesn’t match
“honest.” Choice (A) is the correct answer.

29. E The sentence doesn’t have any clues about the common field
cricket other than the research that belied a common
assumption. Therefore, the blanks will stand in contrast of
each other, so look for answers that contain words that are
opposites. Eliminate choices (C) and (D) since they contain
words that are similar to each other. Eliminate choices (A)
and (B) since neither contains words that are opposites of
one another. Choice (E) is a good fit since kinetic means
“movement” while placid means “not moving much.” Choice
(E) is the correct answer.
30. A Both passages discuss the low sunlight-conversation rate of
current solar panels. Passage 1 explains that because the
silicon can only absorb a narrow band of the solar spectrum, a
majority of the solar energy is lost as heat while Passage 2 also
references the fact that current devices with silicon
semiconductors can only absorb a small band of light from the
sun. Choice (A) fits what both passages say. Passage 1 does
say that a majority of the sun’s energy is lost as heat, but it
doesn’t say anything about the panels overheating, so
choice (B) can be eliminated. Choice (C) can also be
eliminated because, although the silicon isn’t particularly
efficient, it isn’t actually faulty. Choice (D) might initially
look good, but it only addresses Passage 2. Choice (E) isn’t
mentioned in either passage. Choice (A) is the correct
response.
31. A The final sentence of Passage 1 describes why Atwater is
working on the new device, so he would agree with the
statement. That eliminates choices (B), (C), and (E). He
already knows the information—it isn’t anything exciting—
so choice (D) can also be eliminated. Choice (A) is the
correct answer.
32. B Atwater is working on the device; it isn’t available yet. His
statement shows that he feels the research and development

is very promising. Choice (B) is the correct answer.
33. C Passage 1 states that silicon can only absorb a narrow band of
the solar spectrum, while Passage 2 agrees that silicon
semiconductors can only absorb a small band of light from the
sun. Choice (A) is the opposite of what the both passages
state, so it can be eliminated. Physicists are developing a
new solar panel, but the silicon semiconductors are not a
part of that, and the new device is also mentioned only in
Passage 2, so eliminate choice (B). Choice (C) agrees with
both passages. Choice (D) may initially look attractive, but
the silicon is not actually mentioned as a fault, just as a
limitation. There are no mistaken statements, so choice (E)
can be eliminated. The best answer is choice (C).
34. B The initial paragraphs set the scene for the passage’s central
event: Catalina’s meeting with Clara and her growing
interest in politics. Choice (B) best captures this central
event. Choice (A) does not take any of Catalina’s friendships
into account, nor does choice (D), and neither answer is
supported in the passage. And choice (E) addresses one of
Catalina’s friendships, but not the most important one.
35. E The first sentence of the passage reads as follows: The girls in
her room, after a few weeks of getting used to some of her
atypical habits and learning her way of showing friendship,
began to take her in as one of their own. In other words, these
girls had to get used to some of Catalina’s habits, so they
initially considered her foreign or alien, as choice (E)
suggests. The other choices are too harsh and have no
support in the passage.
36. C The full sentence reads as follows: The oldest girl, Araceli,
really started to warm up to Catalina, and she was the first to
invite Catalina into her room for help with homework, to watch
a video clip on the computer, or just to chat about the day. The

three things that Araceli does are evidence of how she took
to Catalina and made her feel at home, as choice (C) best
captures. These are kind gestures, which eliminates choices
(D) and (E). And while Araceli may be beautiful or
intelligent, there is nothing specific in the passage to
support either.
37. E Araceli is the first of the girls to warm up to Catalina,
showing that she is familiar, nurturing, and sympathetic,
eliminating choices (A), (B), and (D) because this question
asks for the answer that LEAST describes Araceli. She is also
described as stern in the final sentence of the paragraph,
eliminating choice (C). Araceli does not seem local to
Catalina, however, she wonders whether Araceli had come
to the big city from a small town like hers, making choice (E)
the LEAST descriptive of Araceli and therefore the correct
answer.
38. A Clara is on her way to a protest when she finds Catalina
reading outside. Clara wants Catalina to join her, as
evidenced by her questions, You coming? And You want to
come to the protest with me? Choice (A) reflects Clara’s
intention. Because Catalina is apparently not responding,
except by joining Clara at the protest, there is no support
for any of the other answer choices, which all suggest that
Clara asks Catalina questions to gain information.
39. B The line containing this simile describes an oddly moved
Catalina, who felt that the sign was a key that had unlocked
something inside of her. In other words, Catalina believes she
has had these feelings and that that they were locked away
inside of her, or hidden, as choice (B) suggests. Choice (A)
describes the sign, not the key. Choices (C), (D), and (E)
provide alternate meanings of the word key, but they do not
work in this context.

40. B Catalina is charmed and flattered that Clara wants her to
come to the protest and that Clara is interested in her
political views. She is not upset by Clara’s questions,
eliminating choices (A), (C), and (E). And while she is
surprised by Clara, there is no evidence that she is
confused, or befuddled, as choice (D) suggests. Only choice
(B), astonishment, correctly captures Catalina’s reaction,
which the passage describes as shocked.
41. A Read the last sentence of the paragraph carefully: She felt for
the first time that she might be able to make a difference for
people like her father. In other words, she is hopeful that she
can make a difference, as choice (A) suggests. Her feelings
are mainly positive, which eliminates all the other answer
choices, which are either negative or neutral.
42. C Catalina’s meeting with Clara was the beginning of a new
phase in her life, one in which she went to every other protest
she could and became as well-informed on the issues as she
could. In other words, by the end of the passage, Catalina
has taken a more intense interest in politics than she had
before, as choice (C) suggests. Choice (B) is too extreme,
and choice (E) assumes that Catalina had gone to political
protests before, which the passage suggests that she had
not.
43. C The author says the effects of orchid farming mirror those of
aloe throughout the world, effects which have produced nearextinction for the medicinal plant. Scientists fear that
orchids could come to a similar fate, lending support to
choice (C). The passage only states that the effects of
farming orchids and those of farming aloe mirror one
another, but there are no other links listed in the passage,
which eliminates all other answer choices.
44. B The word outgrowth appears in this sentence: Some farmers

have had to move to more remote locations or to employ
environmentally questionable methods, but this, they argue, is
not an outgrowth of shortage. In other words, farmers claim
that they are not resorting to these methods because of
shortage or as a response to shortage. Choice (B), effect, best
captures this relationship. Choices (C) and (D) represent
common themes of the passage (overharvest is one of the
practices that is damaging orchid populations, and dearth is
the lack that is created when orchids no longer grow in a
particular place), but they do not apply in this particular
sentence.
45. D The author states that the farmers are closer to the orchids
than scientists are. The author offers as evidence that the
orchid is … essential to life in Tanzania.… Here, the orchid is
just as prized for its nutritional value as for its aesthetic value.
In other words, farmers in this region use the orchid for
more things in their daily lives, and thus have a more
complex, or closer, relationship with it. Choice (D) states
this idea in a very general way. Choices (A) and (C) may be
true, but they do not support the claim given in the
question.
46. D The full statement reads as follows: And the orchid is so
essential to this part of Tanzania, the “Serengeti of Flowers,”
that life is in some ways inconceivable without it. The author
goes on to add that, in this region, the orchid is just as prized
for its nutritional value as for its aesthetic value, as choice (D)
suggests. The other choices use words from the passage, but
the statements in those answer choices are not supported by
textual evidence.
47. C The passage states that the trends in orchid farming mirror
those of aloe farming, but it does not state that the two
crops grow in the same regions, thus making choice (C) the
correct answer. Choice (A) is supported throughout the

third paragraph. Choice (B) is stated in the first paragraph.
Choice (D) is implied in the discussion of Zambia in the
second paragraph. Choice (E) is stated in the first line of the
passage.
48. D The first sentence of the last paragraph states, In the face of
the scientific evidence, some Asian and African governments
have promised measures to protect orchids and the orchid
industry at the same time. Choice (D) gives a very simple
paraphrase of this sentence and of the ideas that follow in
the paragraph. The other choices are not supported in this
paragraph and can therefore be eliminated.

Section 4
21. D First, take the square root of both sides of the first equation
to find that c = 3. Then use your calculator for find 34 =
81. The credited response is (D).
22. D First, list the first seven positive even integers: 2, 4, 6, 8,
10, 12, 14. Then use the average pie to calculate the
average. The sum of the integers is 56; put that at the top of
the pie. The number of things is 7; put that in the lower left
of the pie. Divide 56 by 7 to find that the average is 8. The
credited response is (D).
23. E PITA! Plot the coordinates in the answer to see which makes
the isosceles right triangle. Use the two given points, (2, 9)
and (8, 9), to find that one side of the triangle is 6. Choices
(A) and (C) do not make right triangles. Choices (B) and (D)
make right triangles, but the sides are 3 and 5, respectively,
not 6. Choice (E) makes a right triangle with a side of 6.
The credited response is (E).
24. C PITA! Since the question asks for the “largest integer,” start
with choice (E). The square root of 25 is 5, which is not less
than 4, so eliminate it and move to (D). The square root of
16 is 4, which is not less than 4, so eliminate it and move to
(C). The square root of 15 is approximately 3.87 (use your
calculator), which is less than 4, so it’s the answer. The
credited response is (C).
25. C Label what you know. Since RT = ST, angle R must equal
angle S. Label both angles 75°. There are 180 degrees in a
triangle, so 75 + 75 + ∠RTS = 180. Solve to find that
∠RTS = 30. Now look at the straight line. Straight lines

have 180 degrees, so 30 + x + x + x = 180. Solve for x to
find that 3x = 150, so x = 50. The credited response is (C).
26. E Plug In! In 2 minutes there are 120 seconds, so plug in s =
120 and m = 2. Then plug 2 in for m in each of the answer
choices to find which one equals 120. Choice (E) is 60 × 2
= 120. Remember to check all the answer choices. The
credited response is (E).
27. B PITA! Since the question asks for the “largest integer,” start
with choice (E). Plug in 12 for z. The smallest x and y could
each be is 12. The sum (12 + 12 + 12 = 36) is larger than
14, so eliminate (E). For (D), plug in 6 for z. The smallest x
and y could each be is 6. The sum (6 + 6 + 6 = 18) is
larger than 14, so eliminate (D). For (C), plug in 5 for z. The
smallest x and y could each be is 5. The sum (5 + 5 + 5 =
15) is larger than 14, so eliminate (C). For (B), plug in 4 for
z. The smallest x and y could each be is 4, but they could be
bigger. If x = 5 and y = 5, then the sum (5 + 5 + 4 =
14) could equal 14. The credited response is (B).
28. C PITA! Read carefully and plug the values from the answer
choices into the given equation. Since a and b are integers
less than 5, eliminate choices (A), (B), and (E); they each
contain numbers that are 5 or greater. Plug in choice (C):
5(3) – 4 > (3)(4) becomes 11 > 12. Since this is not true,
the credited response is (C).
29. 4,320 Take it in bite-sized pieces. First, the band earned $15 for
each person, so $15 × 200 = $3,000. Next, the band
earned $10 for each T-shirt, so $10 × 32 = $1,320.
Therefore the total amount earned is $3,000 + $1,320 =
$4,320.
30. 2 To get from 59.43 to 0.5943, the decimal moves two places
to the left. That means that 59.43 is divided by 100.

Multiplying by 10–2 is the same as dividing by 100, so t =
2. Use your calculator to verify.
31. 1,300 Take it in bite-sized pieces. First, translate the first phrase
into math:

of m is 200 translates to

× m = 200.

Multiply both sides by 6 to find that m = 1,200. Next,
translate the second phrase into math:
translates to

of n is 500

× n = 500. Multiply both sides by 5 to find

that n = 2,500. Finally, subtract to find that n – m = 2,500
– 1,200 = 1,300.
32. 40 Write your formulas and label everything. The area of ABCD
is 4, so write the formula and find the side: A = s2 = 4, so
s = 2. Label each side of ABCD as 2. The area of WXYZ is
49, so write the formula and find the side: A = s2 = 49, so
s = 7. Label each side of WXYZ as 7. The area of DCXQ is 4,
so write the formula and find the missing sides: A = b × h
= 16, b × 2 = 16, so b = 8. Label sides CX and DQ as 8.
Finally, to find the area of PDQW, find the side and then use
the formula. Since XW = 7 and XQ = 2, subtract to find
that QW = 5. Now write the area formula: A = b × h = 8
× 5 = 40.
33. 96 One approach is to set up the proportion:
. There are 480 Mint Chocolate
Chip, so
that Pistachio = 96.

. Multiply both sides by 480 to find

34. 100 Extend out the parallel lines and find the angles that are
equal. First extend the parallel lines
and
. Rotate the
page if needed. Notice that line
cuts those parallel lines
therefore all the small angles are the same. ∠DEF = 70, so
∠CFG = 70.
is a straight line, so if ∠AGD = 150,
∠DGF = 30. Next look at the center triangle with a base of
. All triangles have 180 degrees, so the third angle at the
top (next to x) will be 180 – 30 – 70 = 80. Lastly,
is a
straight line, x = 180 – 80 = 100.
35.

138, 276, or 414
Since the number Jen chose was divisible by 2 (even), 3 and
23, it must be divisible by their product: 2 × 3 × 23 =
138. Therefore Jen chose a number less than 500 that is a
multiple of 138: 138, 276, or 414.

36.

.875 or
To make the fraction as large as possible, the numerator
must be as large as possible. Since a – b is in an absolute
value, its value must be as large as possible or as small as
possible. To make a – b large, start with the largest value
for a and subtract the smallest value of b: a – b = 3 – (–4)
= 7. To make a – b small, start with the smallest value for a
and subtract the largest value of b: a – b = (–2) – 2 = –4.
Since the absolute value of 7 is 7 and the absolute value of
–4 is 4, the maximum value of |a − b| is 7. Therefore, the

maximum value of
37.

is

or .875.

or .75
Translate the English into math. The first sentence
translates to 9r + 5t = 6r + 9t. Combine like terms to get
3r = 4t. Then translate the second sentence to t = pr.
Substitute rp for t in the first equation to get 3r = 4pr.
Divide both sides by 4r to find that p =

38.

or .75.

or .25
The question provides the y-intercept, so rewrite the
equation in the y = mx + b format: y =
form, the y-intercept is represented by
intercept is –8, write
or .25.

. In this
. Since the y-

– 8. Solve for d and find that d =

Section 5
1. E The first part of the sentence, In 1900, Wilbur Wright and his
brother, West Side News publisher Orville Wright, journeyed to
Kitty Hawk, North Carolina, is a complete thought. The
underlined portion of the sentence also contains a complete
thought. Since you cannot join two complete thoughts with
a comma, this sentence contains a comma splice error.
Eliminate choice (A). Choices (B) and (C) repeat the
original error and are also incorrect. Choice (D) begins the
underlined phrase with when. However, since the word
when modifies Kitty Hawk, North Carolina, which is a place,
rather than a time, you cannot use when here. Additionally,
the phrase experiments … were begun by them is passive.
Choice (D) is therefore not the correct answer. Choice (E)
fixes the error in the original sentence and does not
introduce any new errors, so choice (E) is the correct
answer.
2. E The non-underlined portion of the sentence uses the past
tense verb was. Since the sentence is discussing a past event,
rather than an event that is currently occurring, the present
perfect verb has begun, which refers to an event that began
in the past but is still occurring in the present, is incorrect.
Therefore, this sentence contains a verb tense error.
Eliminate choice (A). Choice (C) is also in the present tense,
and is therefore incorrect. Choice (B) uses was beginning.
However, was beginning composing and publicly performing is
incorrect; you would need was beginning to compose and
publicly perform. Thus, choice (B) also contains a verb form
error. Choice (D) switches to the future tense by using will
begin, and is thus not the credited answer. Choice (E) fixes
the original error and does not introduce any new errors, so

choice (E) is correct.
3. B The two halves of the sentence are joined by a comma and
the word and. However, in order to join two thoughts in
this way, you must have two complete thoughts. Since the
second half of the sentence uses starting, rather than to start,
the second half of the sentence is incomplete. Therefore, the
original sentence contains an error, and choice (A) is
incorrect. Choice (D) contains a similar error, and uses so
as, which is idiomatically incorrect, so choice (D) is not the
correct answer. Choice (C) contains a comma splice error
and is incorrect. Finally, choice (E) uses effecting in that,
which is idiomatically incorrect, so you can eliminate
choice (E). Choice (B) fixes the error and does not introduce
any new errors, so choice (B) is the correct answer.
4. C If you join two thoughts with a comma and the word and,
you should be joining two complete thoughts. However,
since the first part of the sentence, James Dean, having died
shortly after the filming of Rebel Without a Cause does not
contain a complete thought, choice (A) contains an error.
Choice (B) does not contain a complete thought, and is
therefore not the credited answer. Choices (D) and (E) both
use he, so that the sentence reads, James Dean … he was
only able to receive. The word he is unnecessary, and since
using he changes the sentence so that the subject James
Dean does not have a verb associated with it, both choices
(D) and (E) are incorrect. Choice (C) fixes the error in the
original sentence and does not introduce any new errors, so
choice (C) is the correct answer.
5. C As it is currently written, this sentence does not contain a
complete thought. Therefore, eliminate choice (A). Choices
(D) and (E) similarly do not contain complete thoughts, and
are also therefore incorrect. In choice (B), the clause The
school board is enacting new anti-truancy laws is a complete

thought. The clause they will discourage students cutting class
and encourage regular school attendance is also a complete
thought, although idiomatically the word from should
appear before the word cutting. Since choice (B) contains
two complete thoughts joined by a comma, choice (B)
contains a comma splice error. Choice (C) fixes the problem
in the original sentence and does not introduce any new
errors, so the correct answer is choice (C).
6. A As written, the underlined portion of the sentence contains
a modifier that correctly modifies the subject of the
sentence, Eugene Fama. It also contains a singular verb, is,
which agrees with the subject. Choices (B), (C), and (E)
eliminate the main verb of the sentence. This makes the
sentences fragments, so you can eliminate choices (B), (C),
and (E). Choice (D) incorrectly uses he, so that the clause he
is a Nobel prize winner and one of the world’s most
distinguished economists becomes a complete thought, but
the main part of the sentence—Eugene Farma … many
extolling him as an authority on portfolio theory and asset
pricing—does not contain a complete thought. Thus, choice
(D) is not the credited answer. Choice (A) is the correct
answer.
7. E The subject of the sentence is Tower, which is singular, but
the verb is are, which is plural. Therefore, this sentence
contains a subject-verb agreement error, so eliminate choice
(A). Choice (C) repeats the original error and is also
incorrect. Choice (B) removes the main verb from the
sentence and thus does not contain a complete thought.
Choice (D) changes the meaning of the sentence, and is
therefore not the correct answer. Choice (E) fixes the error
in the original sentence and does not introduce any new
errors, so the correct answer is choice (E).
8. D This sentence gives three items in a list: improved economic

conditions, better health care, and have more social services
programs. Items in a list should be parallel, but the first two
items are nouns and the last item is a verb. Therefore, the
original sentence contains a parallelism error, so eliminate
choice (A). Choices (C) and (E) repeat the original error.
Choice (B) uses with, therefore making the last item in the
list not parallel with the first two, so choice (B) is incorrect.
Choice (D) fixes the error in the original sentence and does
not introduce any new errors, so choice (D) is the correct
answer.
9. C In the original sentence, the first half is missing a verb, and
therefore does not contain a complete thought. Thus, you
can eliminate choice (A). In choice (B), the first half of the
sentence contains a complete thought, and the second half
of the sentence also contains a complete thought. Since
these two parts of the sentence are joined by a comma, this
choice contains a comma splice error. Eliminate choice (B).
Choice (C) fixes the error in the original sentence and does
not introduce any new errors, so choice (C) is the credited
answer. Choices (D) and (E) illustrate the same error as in
choice (A), so they are eliminated.
10. B This sentence contains a list of two things that are
considered cheating: copying and by otherwise using another
student’s work. However, the two items are not in the same
form, and are therefore not parallel. Eliminate choice (A).
Choices (C) and (E) both contain the past tense verb used,
which is not parallel with copying, so both choices are
incorrect. Choice (D) contains the verb to use, which is also
not parallel with copying, so you can eliminate choice (D).
Choice (B) fixes the original error and does not introduce
any new errors, so choice (B) is the correct answer.
11. E The original sentence refers to NASA astronauts as a pilot.
Since astronauts is plural, but pilot is singular, this sentence

contains a noun agreement error. Eliminate choice (A).
Choices (C) and (D) repeat the original error and are
therefore incorrect. Choice (B) contains two complete
thoughts joined by a comma, so choice (B) contains a
comma splice error. Choice (E) fixes the original error and
does not introduce any new errors, and is therefore the
correct answer.
12. D As it is currently written, this sentence compares two
things: paintings from Picasso’s Blue Period and other artists.
Since you must compare paintings to paintings and artists
to artists, rather than paintings to artists, this sentence
contains a comparison error. Eliminate choice (A). Choices
(B) and (C) make similar comparison errors, and are
therefore incorrect. Choice (E) compares paintings to the
same time, and is also incorrect. Choice (D) fixes the
comparison error by comparing paintings to those of, or
paintings of, other artists. Thus, choice (D) is the correct
answer.
13. E This sentence contains the modifying phrase While learning
to ride the new bicycle. The phrase a pink one with green
tassels and a banana seat contains extra information that
simply modifies bicycle. If you eliminate this phrase, you are
left with While learning to ride the new bicycle … a dog. As it
is currently written, the sentence suggests that a dog, rather
than Rebekah, was learning to ride the bicycle. Therefore,
this sentence contains a misplaced modifier. Eliminate
choice (A). Choices (B) and (C) similarly suggest that the
dog, rather than Rebekah, was learning to ride the bicycle,
so both choices are incorrect. Choice (D) seems to suggest
that the fire hydrant, rather than Rebekah, was learning to
ride the bicycle, and is also not the credited answer. Choice
(E) correctly changes the sentence so that Rebekah is the
person learning to ride the bike. Therefore, choice (E) is

correct.
14. D The subject of the sentence is exercise, which is singular, but
the verb is are proven, which is plural. Therefore, this
sentence contains a subject-verb agreement error. Eliminate
choice (A). Choices (B) and (E) also use plural verbs and are
therefore incorrect. Choice (C) uses proven as reducing,
rather than proven to reduce, and therefore contains an
idiom error. Choice (D) correctly uses the singular verb has
been proven, and does not introduce any new errors. Thus,
choice (D) is the correct answer.
15. C The clause It possessed the most advanced safety features
available in its time, and it was generally considered unsinkable
is a complete thought. The clause the RMS Titanic sank along
with 1,500 of its passengers on April 15, 1912 is also a
complete thought. This sentence joins two complete
thoughts with a comma, and therefore contains a comma
splice error. Eliminate choice (A). Choices (B) and (E)
repeat the original error and are therefore incorrect. Choice
(D) uses the word despite, which should indicate a contrast.
However, the phrase possessing the most advanced safety
features available during its time is in the same direction,
rather than the opposite direction, as considered unthinkable.
Thus, choice (D) is incorrect. Choice (C) fixes the error in
the original sentence and does not introduce any new
errors, so it is the correct answer.
16. E As it is currently written, the sentence does not contain a
complete thought. Therefore, choice (A) is incorrect. Choice
(C) repeats this error and is also incorrect. Choice (B) lists
three things that the bicyclists do: pack, travel, and they
participate. Since the three actions should be in parallel
form, choice (B) contains a parallelism error. Choice (D) is
similarly not parallel, as well as passive. Choice (E) fixes the
error in the original sentence while also keeping the three

items in the list parallel, so choice (E) is the credited
answer.
17. A This sentence correctly uses the subjunctive voice by using
the if … were construction. Choice (B) uses the word instead,
which is redundant since the sentence already uses rather
than, so choice (B) is incorrect. Choice (C) uses the future
tense verb will, which you cannot use with the word if, so
choice (C) is not the credited answer. Using the subjunctive
voice and the word if requires were plus the infinitive form
of the verb, rather than the present tense, so choices (D)
and (E) are incorrect. Since the original sentence does not
contain any errors, choice (A) is the correct answer.
18. A The correct idiom is regardless of whether, not regardless of if.
Therefore, eliminate choices (B) and (D). The phrase
whether or not in choice (C) is redundant, and the singular
pronoun it doesn’t agree with the plural noun belongings, so
eliminate choice (C). Choice (E) also uses the singular
pronoun it, so eliminate that choice as well. The correct
answer is choice (A).
19. E The modifying phrase Famous for founding the world’s first
private detective agency should modify whatever appears
immediately after the comma. However, as it is currently
written, this phrase modifies another fact. Since it is Eugène
Vidocq, not a fact, who founded the detective agency,
Eugène Vidocq should appear immediately after the
comma. Therefore, eliminate choices (A), (B), and (D). Note
that in choice (C) Eugène Vidocq’s career, rather than Eugène
Vidocq, appears right after the comma. Since the man,
rather than his career, founded the detective agency,
eliminate choice (D). Choice (E) fixes the error in the
original sentence and does not introduce any new errors, so
choice (E) is the correct answer.

20. B As it is currently written, this sentence compares The reigns
of Atilla the Hun to many other early rulers. Since you need to
compare reigns to reigns, rather than reigns to rulers, this
sentence contains a comparison error. Eliminate choice (A).
The subject of the sentence in choice (A) is reigns, which is
plural, but the verb is was, which is singular. Choice (C)
therefore contains a subject-verb agreement error and is
incorrect. Choice (D) repeats this error and is also incorrect.
Choice (E) uses the past perfect verb had been. Since this
sentence does not contain two past events, one of which
occurred before the other, the past perfect tense is incorrect
for this sentence. Eliminate choice (E). Choice (B) removes
the incorrect comparison and does not introduce any new
errors, so choice (B) is the correct answer.
21. B This sentence lists three things that the author wants to do:
traveling, skiing, and to swim. Items in a list should be in
parallel form, so choice (B) contains a parallelism error,
since to swim should be swimming. Choice (B) is therefore
the correct answer.
22. C As the sentence is currently written, the singular pronoun it
refers to the plural pronoun visits. Therefore, choice (C)
contains a pronoun agreement error and is the correct
answer.
23. E Choice (A) correctly compares the stories of other authors to
those of Vonnegut. Choice (B) is the correct verb, choice (C)
is the correct adverb, and choice (D) is the correction
conjunction. Therefore, there are no errors, and choice (E)
is the correct answer.
24. D The correct idiom is originate in, not originate from. Choice
(D) is the correct answer.
25. B The word significant is an adjective, but it modifies

influenced, which is a verb. Since adverbs, not adjectives,
modify verbs, choice (C) contains an error; the correct
modifier is significantly.
26. D The pronoun early in the sentence is one, which is singular.
The plural they in choice (D) does not agree with one.
Therefore, choice (D) is the correct answer.
27. B The main clause in the sentence, The Montreal Biodome being
composed of four zones, does not contain a complete
thought, since the verb is being composed. In order to make
the thought complete, the verb must be changed to is
composed.
28. E Choice (A) correctly uses an adverb to describe an adjective,
so there is no error there. The plural verb have made in
choice (B) agrees with the plural subject rules. The singular
verb has in choice (C) agrees with the singular subject he,
and choice (D) does not contain an error. This sentence is
correct as written, so choice (E) is the correct answer.
29. B The sentence is discussing different types of stars, and is
therefore discussing plural items. However, a temperature is
singular and does not agree with types of stars. Correctly
written, choice (B) should read different temperatures. Thus,
choice (B) contains a noun agreement error, and is the
correct answer.
30. A Because the verb in the non-underlined part is past tense,
the future tense in choice (A) creates an error in tense.
Choice (A) is the correct answer.
31. C The pronoun it does not clearly refer to any one noun; it
seems to replace predicted, but since you cannot use a
pronoun to replace a verb, the pronoun it cannot replace
predicted. Therefore, choice (C) contains an error.

32. C The verb sits is singular, but the subject of the sentence is
the Great Temple of Ramses II and the Small Temple of
Nefertiti. Two singular nouns joined by the conjunction and
make a plural subject, so the subject of this sentence is
plural. Therefore, this sentence contains a subject-verb
agreement error, and the correct answer is choice (C).
33. A The correct idiom is insisted that, rather than insisted to. In
order to read correctly, the sentence would need to read
Frank insisted that he be allowed to present his paper at the
conference, or something similar. Therefore, choice (A)
contains an error and is the correct answer.
34. B Use less for items that are not countable, and fewer for items
that are countable. Since residents are countable, choice (B)
contains an error.
35. B The subject of the sentence is spending, which is singular,
but the verb is are, which is plural. Thus, this sentence
contains a subject-verb agreement error. Eliminate choice
(A). Choice (C) also has a plural verb and is therefore
incorrect. In choice (D), the word that does not clearly refer
to any single noun, so choice (D) is incorrect. Choice (E)
fixes the subject-verb agreement error but is unnecessarily
wordy. Choice (B) fixes the error by using the singular verb
is and is more concise than choice (E), so choice (B) is the
correct answer.
36. D As it is currently written, the sentence seems to suggest that
the fact, rather than studying irregularly, is the worst action
you can take. Therefore, as it is currently written, the
sentence contains an error. Choice (B) uses the word such,
which would imply that irregularity was discussed in the
previous sentence. However, since that is not the case,
choice (B) is not the correct answer. Choice (E) uses the
word so, and thus contains a similar error. Choice (C) is

unnecessarily wordy and uses the word being, which is often
used incorrectly in PSAT grammar questions. Therefore,
choice (C) is not the credited answer. Choice (D) fixes the
error in the original sentence, and does not introduce any
new errors, so choice (D) is the correct answer.
37. E Since those who practice speaking in a foreign language do
not literally become children again, since their ages do not
change, the word literally is not used correctly in this
sentence. Eliminate choice (A). The sentence does not
discuss a contrast, so both choices (B) and (C) are incorrect.
The sentence does not contain an example, so choice (D) is
not the credited answer. The sentence is attempting to
explain that those who practice speaking in a foreign
language often speak as if they were two year-olds, so
choice (E) correctly captures the intended meaning of the
sentence, and is the correct choice.
38. D The end of sentence 11 mentions that individuals practicing
a foreign language are likely to make mistakes. Since
sentence 12 shortly thereafter mentions that they are likely
to occur, they most probably refers to mistakes. Thus, the
correct answer is choice (D).
39. D The passage as a whole discusses the process of learning a
new language. With the exception of sentence 8, each of the
sentences in the answer choices discusses some factor
related to studying a foreign language. However, sentence 8
introduces the idea of learning to play an instrument, which
is unrelated to the topic discussed in the rest of the passage.
Hence, the correct answer is choice (D).

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